It's hard to the answer the question without knowing anything about the players to act after you. But I think, on average, you need to raise. Nothing wrong with everyone after you folding and improving your chances for a scoop with your Aces. And similarly there is nothing wrong with everyone calling and building a monster pot that you might be able to scoop.

Also, I don't get the river check at all. Bet and try to take the whole thing. He doesn't have a flush. With your aces, he probably does not have nut low. So he's either on something like 2-3, or maybe a 2-pair that might be folded to a bet.