Monster design, including loot, is top down. That is to say, you start with the end goal in mind, of which narrative sense is usually a part, and choose numbers and loot that fit what you, or the designer wants to accomplish.
Consulting the gamemaster's guide on monster creation, under items size is not considered specifically. Instead, the focus of that section is entirely on player wealth.
If for thematic reasons the monster wields a weapon that is unusable for the players, it's potential impact on player wealth should still be considered - for them, it may as well be objet d'art. In fact this might be a creative and thematic way of providing your characters with money!
However, the section on monster damage does consider monsters wielding manufactured weapons in the sidebar, but again primarily from a top down perspective; what are the your/the designers goals, for this monster, and this encounter?
In general, the monster's overall damage is balanced for the encounter, rather than the specific weapon. If the monster is themed as wielding a tiny dagger, then it has abilities that compensate for the dagger's low damage.
The final paragraph of the sidebar may be particularly relevant for some GMs considering this question, and wanting to give a Giant Instinct Barbarian a cool weapon;
On the flip side, you might want to use a one-off creature as a source of a particularly high-level piece of treasure, such as a magic weapon. In these cases, you might want to make the attack bonus higher for the potency rune or the damage higher for a potent striking rune so the PCs feel the weapon’s effect before they obtain it. This will make the treasure feel more powerful, since they’ve already been on the receiving end.
N.b. As a GM, I generally require armour to be adjusted to fit players before they can comfortably use it, via a relatively simple crafting check and time, even when taken from a humanoid of the same size category. I'd probably allow something similar - with a more substantial crafting check if they decided they wanted a giant's armour.