1/2 Stars QQ, deep, interesting

[Proofrock]

I think you can pretty safely fold the river.

The small preflop raise could be a pot-sweetener with some suited connectors or a low pair (though a little unlikely with low suited connectors because of the shortstack limper) or something like TT+,AJs+,AK,KQs. You're both deep, so his call preflop doesn't narrow this range much.

On the flop, nothing changes. On the turn, though, I figure this could be an overpair (less likely because he checks twice and I don't expect him to check-raise any overpair lower than QQ), trips (also unlikely based on p/f range), a boat, an unlikely straight, or a turned flush draw that expects he can take you off your hand based on your weak bet.

After you call the turn, it seems really unlikely that he's going to try to push you off your overpair. Since the flush draw also got there if he didn't have you on the turn I think he has you now. Given the river, I expect he'd check or make a smaller blocker with almost everything that you beat. If I call I expect to see a flush, a boat, or AA (in roughly that order).

---
Given your description of Villain, I would have prefered to bet the flop, check the turn, call or value bet the river. I don't like checking the flop because your hand is relatively vulnerable, and he doesn't seem likely to run a big multi-street bluff OOP vs. you with deep stacks (so you can pretty safely get away if he gets aggro while still extracting value when you're ahead).

As played, I'm not crazy about the small turn bet. Also, I haven't thought too carefully about it, but there may be value in 3betting the turn.