After reviewing this hand, I made a simple CREV simulation to better understand my EV here. So, assuming that my opponent calls or raises this: ( >=middle pair, flushdraw, gutshots or more, Ahigh + bdfd) and folds everything else (1 over trash, 2 overs trash including AJ without bdfd, and pockets under 7), he calls 57% of hands and folds 43% of hands.

Real opponent had 49% fold to flop cbet OOP, so I think number of 43% is fair.

This way, my immediate EV of betting is 0.27, and by immediate EV I mean that to simplify my simulation I fold every turn. So even without outs to A, its good to bet here.

There are 2 problems with my analysis:
1) If opponent calls flops slightly more than 57% of time, for example he calls all pocket pairs, my bet turns out to be -EV, not including later streets.
2) Even if my EV of betting is better than 0, it might not be better than EV of checking, because by checking I generate some equity on my outs (Aces and sometimes Deuces) and have small SDvalue against Khigh and Qhigh.

What is you line here with weak Aces?