I would 3-bet the flop to see where I'm at. As played, villain could easily have A6 (turned the boat, why not slow-play) or A8 (raising for info on flop and hoping for a free card).

I would also check-call a moderate bet on river. If you lead out, better hands will call or even raise you, and worse hands will fold. If you check the river you can perhaps induce a bluff. Even if he has you beat he might not have bet as much as $0.5 which is what he's now raising you by.