In the interests of balance and simplicity, some flexibility is lost
Pathfinder 2e removes the capability for Small/Medium ("Standard") creatures (read: PC-like) to wield particularly odd-sized equipment. There are no rules whatsoever about Tiny/Large/Huge/Gargantuan creatures because the GM's should be making their best judgement regarding them. For me, that would mean treating the weapon as either unable to be used, or it's Light/Heavy version if available.
Currently, the only way for PC's to 'break the mold' on Small-Medium sizing is to be a Tiny Sprite. Information on Sprite weaponry fits with the rest of the description, from Tiny PC's
You can purchase weapons, armor, and other items for your size with the same statistics as normal gear, except that melee weapons have a reach of 0 for you (or a reach 5 feet shorter than normal if they have the reach trait).
GM's are expected equip their monsters and such with appropriately sized weapons; otherwise, they can also gloss over their ability to use them with special abilities and/or penalties accounted for in creature creation.
Bonus damage from size is included in attacks' flat bonus, such as that granted by Enlarge or lack thereof, such as in Shrink. Even Gargantuan creatures use standard weapon dice (here, their striking longspear does 2d8 damage and their greater striking greatsword does 3d12)*. Creatures from the Bestiaries should have modifiers to have them deal an appropriate amount of damage included, and the Building Creatures section has allowances for a range of damage quantities; High or Extreme can be used for particularly large creatures; it also includes that GMs can play around with the die/modifier combo that averages to the given number.
On Table 2–10, you'll find a damage expression (a die roll or rolls plus a flat modifier) you can use as is, or you can take the damage in parentheses and build your own damage expression to hit that number. If you do the latter, remember that a d4 counts as 2.5 damage, a d6 as 3.5, a d8 as 4.5, a d10 as 5.5, and a d12 as 6.5. Usually a damage expression works best when roughly half the damage is from dice and half is from the flat modifier. If your creature deals special damage, like 1d6 fire from flaming attacks, that counts toward its total damage per Strike. Keep in mind that a creature using a weapon should have a damage value that feels right for that weapon. Extreme damage works well for two-handed weapons that uses d10s or d12s for damage. On the other hand, a dagger uses only d4s, so a dagger wielder would need something like sneak attack to deal extreme damage, or you might compensate for the dagger's lower damage per Strike by giving the creature the ability to attack more efficiently or use other tricks.
*Either the Titans have misprints in their weapons or they gain one additional die on weapon attacks.