AQo 3bet pot

Preflop is ok.
Flop bet is fine.
The turn depends on the villain:
- if he is an aggressive player you might want to consider a check/raise.
- if he is a passive player you want to bet to get value from flush draws, straight draws, top pair, two pairs...
I would bet small on the river - probably 20 or 30% of the pot to get value from paired hands that missed their straight. I also think it is correct to fold to a raise - there just aren't a lot of hands that bluff there.

Preflop fine.

You hit a straight there and I think this is quite normally a 3barrel broke hand if nothing special happens. I wouldn't get fancy and start check raising the turn if I don't know for sure that villain is aggressive and gets induced by a check.

I think this board could hit quite nice BTN's calling range. He could have lower straight and a lot of 2pair or pair+draw type of hands. You are slightly deeper than 100bb. I would probably in this situation increase the flop sizing so I could get the stacks in more comfortably. I think one decent option could be betting the flop closer to pot size and then making a small overbet jam OTT?

As played I'm not thrilled about the flush completing and you making an overbet shove. Does he call that with weaker hands? I might go with a thin value bet and fold vs a raise or check call.

You could have bet bigger OTT and maybe slightly OTF but whatever. I prefer jamming because check/folding sucks and check/calling isn't great. At least by jamming we are valuing thin, he can totally still call stuffs we beat that he'd check back he we check.