Fate has allowance and precedent for weakness, and primarily that comes in two forms I've seen. I'll get to how to pull them off, but they're these:
- Creatively leave a blank in your character's capabilities, and design around it deliberately. This goes beyond simply not putting a point somewhere, and can be quite fun to work with and design.
- Create opportunities for compels and for things to go badly when you engage in something, because you don't do that thing well. This can involve more than setting up the right aspects.
I'm not aware of much precedent for simply adding -2's. Fate doesn't tend to deal in negatives much. I wouldn't say that's necessarily a bad idea though, maybe it's fine! I haven't seen it or played with it though, and maybe authors have just decided to go with the positive flow.
Now, pulling this stuff off. I'm going to explain in reverse order, because the compels thing is simpler, and the other option builds on it. My examples will mostly be using the Atomic Robo RPG, the Fate implementation of the Atomic Robo comic, because that's where I've really been able to play around with this stuff.
Opportunities for compels
A good aspect on its own will often be a double-edged sword that can be compelled to your detriment - character flaws such as impatience getting in the way of your work or attempts to succeed. Use the heck out of these, and build your weaknesses directly into your character's behaviour. (Of course, this can also be invoked against you to make things harder. Do this! But compels tend to be an even meatier way to express a weakness.)
Atomic Robo goes a bit further than this, and introduces some mechanical bits you might want to ransack: costs and weaknesses. They're designed to reduce the value of a stunt so you can take more, and certain extra-powerful stunt types must be coupled with a cost or weakness, but they're fun in their own right for the havoc they can cause, and they ask the GM to help things go worse for you.
- Weaknesses are attacks and effects you're vulnerable to. Atomic Robo has a fear of insects and a weakness to electromagnetism, Daredevil's weak against overwhelming noise, etc. Pick interesting things you want to see used against your character.
- Costs are a more generic invitation that when you use the stunt that involves a cost, something should go wrong. Super-strength? Compelled to break something, or you become doing it, or you might lose control of yourself. Great with a sword? Your demonstration might actually frighten some people, or you might choose to demonstrate on the Duke's heirloom drapes.
Building around blanks
This can be as simple as not giving someone a key stunt: don't give them Empathy, or don't give them Shoot, and so on. Deliberately leave them without strength in areas that could be important.
Where this gets more fun, though, is when you add a stunt to compensate in specific ways, so that they can only approach that area of weakness from a strange angle or one that causes as many problems as its solves. One of ARRPG's suggested stunt types is one that lets you use one skill in place of another for a specific purpose: for example, use Computer Science instead of Empathy to create social advantages when dealing with a robot. This is something you can play around with:
A prewritten stunt lets you use Deceive instead of Empathy or Rapport when you're in disguise and acting in character. This can leave you with someone who is inept at making friends or reading people - but comfortable doing it as long as they're pretending to be someone else. (This stunt was used by a rather creepy secret agent in one of my games.)
I've chosen to take a similar stunt for a Charles Babbage character — a statistician who invented the computer, but whose idea of parlour conversation was reciting trivia. He can use Mathematics in place of Empathy to create advantages and overcome, but at a cost: and the suggested cost is that he offends someone, possibly the person he's talking to. The stunt name is Let me explain why you're wrong.
Likewise, dig out stunts that let you apply what you're good at in strange ways - or ways that will work but help things go wrong if you use them.
Craft weaknesses, in other words, by either simply not investing in competency, or by creating effects that will make things go wrong when you try what you're not good at, and which will in turn make the game more interesting.