We know, thanks to the DMG (p. 278), that a creature has disadvantage with a weapon sized for a creature larger than itself - but the wording is less clear concerning the damage. Do weapons looted from larger creatures deal the same amount of damage as normal when wielded by Medium-sized PCs?

My reading is that the increased damage is considered (mechanically at least) to be due to the weapon being oversized, rather than the wielder, but I would like some second opinions. (RAW and RAI interpretations are both welcome.)

Would a Medium-sized creature, specifically a Monk PC, wielding an oversized (large) spear deal 2d6 damage on a successful hit? Furthermore, would a Large creature with a Huge spear deal 3d6? (And so on.)