I would call , id cbet the flop aswell with bdfd and bdst with the overs , 1/2p is good enough and then just set up a river shove with the turn sizing

Versus this kind of player I usually cbet the dry-ish flop and continue on that turn.
As it went, it's a call for me.
I didn't bet the A turn which means my hand is now disguised somewhat. I think folding would be a mistake but I think shoving it all in now might be overplay with just a one-pair hand and we'd see 2P+ or a str too often.

This is a crying call as just not enough of what the villain is repping makes sense apart from 555 or A5 but that is just unlucky if so as we block one.

Flop you are better to bet than check as we get hands with equity vs ours to fold such as small pairs and also even just random any 2's. Also we can rep lots of turns and rivers or just barrel it off.

I prefer a cbet here on a dry board with two overs and and backdoor flush draw. Even fish play more straightforward in reraised pots, and you'll protect your hand against anything with equity that might give up if you bet.

As played, I've learned my lessons a long time ago with calling river raises with non nutted hands, even against bad players. This guy has a huge gap between his VPIP and PFR which indicates usually a passive tendency. Unless you have evidence that he will do this with AQ AJ type hands then I would give it up. I don't care if the pot odds are good.

Has he made any post flop raises so far?

Flop check call here makes about as much sense as taking a cat to your local swimming pool.