Two things:
You obviously don't call that river bet unless you can see his hole cards.
Make a note that you are up against a fish. Not because he overbet the river (you are the fish on that street), but because he slowplayed a AAA set on a very drawy board (and limped with AA). Only EXTREMELY bad players do that.
EDIT: Actually, we should all be very careful about who we label as fish. I have see so many threads where people have been OWNED by fish, reasoning something along the lines of "he can't have a good hand because he's a fish - therefore I call 300 bb with my top pair".
Sure, fish are fish, but they rarely actually hate money or have a low IQ, and what they do makes sense to them. Your job is to figure out their rationale for their moves. This isn't always easy.
EDIT AGAIN: This shows that making a few "mistakes" in poker can be turned into profit. There's nothing wrong in once in a while making bad calls when drawing (as long as it is reasonably cheap). Your slight loss of EV can buy you a tremendously profitable FISH IMAGE. They see you make these bad calls, but don't realize you usually play rationally.