I was really unsure of what to do on this hand. This hand came up during the PLHE part of the tournament, relevant info:
Image: Nitty, maybe even weak/tight. Villain is 40-50 yr old solid player, not sure if he knows who I am or not that would impact my image at all.
History: We've only played one significant pot together, during PLO. He limped UTG I potted from the CO with QQT7ds diamonds and spades. Flop was T42 all diamonds. Action went check/check, he bet pot on turn (Kh) and I called, he bet pot on river (Ah) and I tank/folded as he had been playing relatively tight up until that point. After folding he flashed the Kd. I tanked long enough it was somewhat obvious I had a tough decision, but not sure if thinks I'm a hold em donkey who couldn't decide to fold AAxx there or folded something like I had.
Villain Image: Mid 40s/50s guy. Had been playing fairly tight, but not super nitty and not weak tight. Had played most of the pots he had been in strongly making pot sized bets or check/folding for the most part. He had played one hand in the PLO section where he flopped middle set against a player who obviously had AAxx and check/called his flop push, but that seemed pretty standard and I hadn't seen him show anything else but that Kd. Had never check/raised up until this point. He also seemed to show a basic understanding of pot/implied odds playing a more hands with more players in the pot, particularly from the button and blinds, but I hadn't seen him show anything down yet.
Hand. 50/100 PLHE I was dealt A

A

in middle position. Folds to me and I raise to 300. Terrible calling station two to my left calls, Gavin Smith calls on the button, decent player in small blind calls, and villain mentioned above calls in the big blind.
We start this hand with ~11k, villain has us covered.
Flop (1500): J

3

2
Checks to me. I make it 750 (which in hindsight I think is a little small here). bad player folds, Gavin folds, SB folds, BB rather quickly makes it 1500. I call
Turn (4500): 3
Villain bets pot. We have ~9k left.
What do we do? If it influences the decision at all, the table seems pretty soft during PLO and probably about average during hold em. I had one of the best seats at the table though with most of the better players (Gavin being the obvious exception) directly on my right. Comments on all streets welcome and appreciated.