Theme is very important, but is only one dial you have at your fingertips. A serious theme makes for a serious game, but not all themes that are interesting are inherently serious. For neutral themes, neither inherently silly nor inherently serious, there are still lots of small ways to bend the game toward gravity rather than levity, and they can add up.
One powerful framing tool you have is scene questions. What does your game ask about itself? What brings out nobility and sacrifice are tragedy and (mild) horror. Think of the tragedies of stories and history: betrayals, loss, conquest, oppression. You don't have to make your game an unending parade of the worst of human nature, but using these as a judicious seasoning can push a game toward more serious moments. "Why did the queen poison her own son, the heir to the kingdom?" is a question that will not guarantee a lack of silliness, but it forces the scene to be, at least partially, about human struggles and emotion. (Or Martian struggles and emotion, same thing.)
One of the more subtle things you can do is seed the palette with things that make the game "grittier" or "more realistic". We once played a game, The History of the Ant Queendom from the Age of Myth to the Sidewalk Reno Apocalypse. It was a game that had a lot of potential for silliness, and everyone but myself was new to Microscope (and new players often go silly while getting a grip on how it plays). One of the things we put on the Palette that made the game more serious was "No: anthropomorphisms". So we had an civilisation of sentient ants that we were going to play, but we had to make them ant-ish, not just humans in ant shape. It forced us to think in terms of real ants, modified only as much as we needed in order to make them characters that were meaningful and interesting to play.
Using the Palette to ground a game's sensibilities is more of an art than a science. Think of the genre you've settled on and what it commonly incorporates as fantastic elements. Then either put those on the No Palette or put a more grounded, pedestrian, or grim version of it on the Yes Palette. Playing space opera? "No: Psionics; Aliens". Fantasy? "Yes: Magic comes from only demons", or "No: Non-humans". You don't have to ban silliness outright (and it's hard to anyway), but you can use the Palette to shape the ingredients you're going to use, giving the whole of them the feel you're going for.
Another traditional item on our Palettes when we're feeling more serious is "No: Clowns". It's not a solid preventative measure, but more of a signal that we're going to avoid the extremes of silliness. You might find "No: Absurdities" to be more pointed, but whatever gently redirects your group's thoughts from the silly stuff will work to subtly influence you toward a more serious game.
One of the knobs you can tune is what you introduce to the game on your turn.
One of the problems with a wide-open game like Microscope is that players feel a significant pressure to be creatively interesting at every moment, and end up forcing themselves to think of outlandish absurdities just to make things different. Instead of the king living in a sombre stone castle where he can reasonably have excitingly mundane problems like assassins and traitorous pretenders to the throne, we get a crystal city on the back of a flying turtle ruled by the Omnipotent Goblin Sultan. Difference for difference's sake is rarely good and solid to build on, and the group will struggle to form a holistic, integrated vision of this place as a real and believable place. That lack of being able to believe in the game objects results in a detachment and lack of investment, which, coupled with the precedent of absurd details, can easily precipitate a carelessness that spirals into yet more absurd details.
The cure for this is being boring. Okay, not really boring, but "boring".
Boringness is actually not a sin when you're playing a roleplaying game. One of the bits of advice form Graham Walmsley's roleplaying handbook Play Unsafe is when you are improvising what comes next, to do the obvious thing. The wondrous thing about a group activity like an RPG is that what is obvious to one person will be unobvious to another. The strokes of genius that you see in other players are rarely carefully crafted to be genius – they're just what they boringly thought should happen next, but it's fresh and unexpected from the different perspective that you inhabit. With three or four people around the table just doing what they think is sensible and boring, you'll constantly hear unexpected and clever things from your fellow players. And best of all, when they're "the obvious thing", they are things that are well-tied and grounded in the world you're creating, giving them a solid reality that you can all invest in properly. Lack of silliness is not so much the way to a serious game, as much as it's your investment in the trials and tribulations of these people.
Being boring applies to creating Periods, Events, and Scenes, as well as in all the details of setting up the scene and when playing the scene out. Don't strain to find something clever; just do what you think makes sense. Don't avoid clever when it occurs to you, but don't stretch and struggle for false cleverness. It's not necessary, because the obvious thing is likely to be perceived as clever anyway. And besides, often enough pushing for cleverness just comes off to others as trying too hard and it falls flat. Go for boring and you'll get nuanced, human drama more often.
When setting up a scene, it can be tempting to leave the character choices wide open, but they're an opportunity to set the tone of the scene. A scene on an airship could involve the dashing swashbuckler and his trusty gorilla companion, or it could involve the Pope and a wounded Spanish ambassador. Which is going to put your fellow players in a less silly mindset when they choose characters and thoughts?
Use your authority to set characters to place people into the game who have mundane, grounded problems. The space fleet admiral and the ensign she's cheating on her husband with. The aging CEO and the assassin come to kill him. President Bear and the cruel trainer from his circus days so long ago. The clown and his estranged father. Almost any character, no matter how inherently silly, can have human drama attached to them by the relationships that are implied by the character they're paired with.
Scene thoughts are extremely powerful ways to shape the fiction. Have you got a President Bear, a presidential aide, the Secretary Bird of State, and the First Ladybear? Could be silly. But as soon as the player playing the aide thinks, "I will uncover the traitor among us and report back to my true master," suddenly the tone and direction of the scene has been irrevocably altered. Again, this alone isn't enough to turn a silly game into a high drama, but along with all the other techniques available, this can build on those and direct the tone of the game toward drama and away from comedy.
The Focus is a very powerful way to set the tone of the game. Is the Focus going to be pie, or is it going to be unrecognised nobility? The Focus is what the round is going to be about, so give it implied gravity and drama.
The First Lens
The first Lens of a round has the power to create two cards, so there is more ability to shape the round's tone. The first Lens of the entire game has even more influence over tone! The advice for teaching the game (p. 60, "Be the First Player") is as valuable when trying to set tone as it is when trying to teach new players. Do as it advises: start very specific, with a bang that will kick the game into motion, and aim to create a Scene.
If there is a good, promising Event someone else made that could be full of drama and seriousness, choose that to build on. It will give them a bit of an ego boost associated with a more serious tone, which will give them some positive feeling about playing out drama. If there is no suitable Event, use your ability to make two at once when you're the Lens to create an Event that implies drama and set your first Scene there.
Use all the previous advice (but beware! don't end up trying to hard! use only what makes sense and is "boring"!) to make that scene kick the game off with a tone of excitement and human-scale drama. In that ants game I mentioned, I started the game off with the Event The First Ant Crosses the Ocean and then a Scene with the first Queen riding on the back of Crow, having a deep argument about the nature of the world and magic. It significantly set the tone of the game. Even when someone else introduce Ant Magic to the game, it was set in the Age of Myth period and took on the solemn, otherworldly tone that I'd established with that first scene.
The (Sorta) Nuclear Option: An Different Group (Sometimes)
Microscope is a fascinating game, from a sociology viewpoint. I've played many games, every single one with a different mix of players, and every game has been subtly but powerfully influenced by the different personalities around the table.
I've played in a game that was about genome-manipulated slave soldiers, because of the input of one player who thinks about human rights issues a lot. I've played a game where Juggalos became the dominant spacefaring culture in a galactic Empire, because one silly player put them in the Palette. There was a game about Mythic Vikings full of war and bloody axes, because I'd recently visited Sweden and Iceland. The very same weekend I played in a game about superheros in the Renaissance, where the Pope could turn shoot lightning and Arthur Pendragon was an actual dragon, while Leonardo could split off clones of himself to better build his airships and other inventions, because someone wanted supers and another wanted an unusual twist on the genre. A game with the author was full of rebellion, terrorist bombings… and in the last scene, one unremarkable scientist who took the lethal Godhead drug in order to super-compute how to end the war, but when he saw that the insight he'd gained would also destroy his wife's memory of their love, chose to take the secret to his grave. One game with some of my regular players was about royal ants and the Black Ant war when I played with them, while a game they played that I was absent was all about cartoons coming alive and fighting Nazis. Then there was the generation ship game with Brian, which was by turns deadly serious and absurd, but the absurdities were always the sort that you find in science-fiction where the people are doing ridiculous things (in the audience's opinion) only because they've forgotten their own history.
The point is that that mix of players in a game is very much the alpha and omega of the tone, and the way the game distributes authority means that everyone puts some of their style and tone preferences into the game. You, through clever use of the dials the game gives you can maximise your influence over the tone, but it will never be yours alone to determine. You can bend and twist the sillinesses into seriousnesses (as I did with the game about Juggalos in Space), but why make it such hard work?
One of the easiest ways to enjoy Microscope with different tones is to play with different groups. Find some gamers who are more into human-scale drama and see what Microscope is like with them. The wonderful thing about this game is that it's so painless to get running with a new group that you can play with with a different set of people each time, unlike RPGs that need considerable setup. And you can play it as a one-shot, so you can lure in gamers who would otherwise balk at committing to a drawn-out campaign using a weird new game. I've had great success playing Microscope with non-gamers as well, since it has none of the baggage of traditional RPGs that can so easily confuse new players and which is so hard for us to teach because we take it all for granted.
Build on Silly Things
This is more of a general directive – the specific techniques above are all useful for this. Build on what the silly players add. If they add something implausible, ask yourself "How does that actually work?" Ask yourself questions about what these silly things would imply in a serious universe, and explore their dramatic consequences.
Are there pink bubble-blowing dragons futilely threatening the realm? Okay, that's kinda ridiculous. But ask yourself: How does their biology work? What force drives them to suicidal attacks against the knights and trebuchets they die to? What tragic figure, forgotten in history, worked their wizardry to create these things? When the rare knight dies in a bizarre pink-bubble-blowing fight, what do the funerary rites look like? In a realm with no credible outside threats, what sort of infighting and treachery do the nobles feel safe to engage in? For every silly thing another player adds, you can ask yourself questions about how it's actually perfectly sensible in a believable, serious world. Ask those questions and you'll suddenly find the soaring flights of fancy being tied to the ground in nicely integrated ways that build on and honor the other players contributions rather than ignore or work around them.
A Worked Example
The Juggalos in Space game is a good working example of some of these principles. It was made silly from the outset when one player added Juggalos to the Yes Palette, yet me being a gamer who likes him some serious drama managed to put a lot of drama into that game that we all enjoyed, and without banning silliness. Despite tentacle monsters, robot sex scandals, and a planet named Faygo, we managed to have a Imperial succession drama, a sinister immortal robot destroying the wormhole network for secret noble but tragic reasons, a space trade republic slowly going evil or decadent (we didn't learn which), and questions about the rights of sentient robots and their relationship to their human creators. It doesn't go into detail about all the possible techniques, but it does serve as an example of how silliness and seriousness can co-exist in the same game with some deliberate choices and techniques.