A small character with 8 strength has a heavy load limit of 60. "A character can generally push or drag along the ground as much as five times his maximum load. Favorable conditions can double these numbers, and bad circumstances can reduce them by half or more."
So he can drag 300 pounds, I daresay at least 600 underwater. I think at 15 feet per move action (walking along the bottom?), but I could very well be wrong there.
Btw, since stunned creatures can take no actions while stunned, the poor fellow isn't holding his breath. Again I might be wrong, but I'd count holding one's breath as an action of some sort, even if it's a free one. But that is a bit too cruel maybe, especially if it'll take time to get out.
Holding your breath isn't an action, actually.
He'd sink though because he can't make a Swim check to stay afloat in the same spot.
My question is this, does the buoyancy effect of water have any affect on the small character's encumbrance and carrying capacity limits?
Encumbrance and carrying capacity would be unmodified.
You might want to only count a fraction of the stunned characters weight as being actually carried or lifted by the small character due to buoyancy. However, these physics are not adressed by the rules.
I would say no.
While the buoyancy would lessen the weight of the character, as far as lifting, dragging and pushing weights, you are severely limited by not having a solid surface to support you.
IRL, I would choose to carry weight around on ground than in water. While a log of wood or a human corpse could be pushed, while it floats, and person with several kilos of equipment (probably armor) is going to drop down.