[Timor]

A 37/22 doesn't strike me as the type to fold TP at any point, especially because he seems to fold to 3bets a lot.

Fact remains that his range seems pretty strong and I think 3 barreling vs that range is a losing play. The fact that we have Ah doesn't change a lot in terms of fold equity (which is what should be the tipping point between cbetting or check/folding, bare equity/implieds are less relevant here I would say). If anything he might continue lighter on a heart turn because now we can have all the flushdraws in our range to barrel. If I have AQ in his spot and I get 3barreled on a heart turn and blank river I would be hard pressed to fold. Sets,KK-AA obv never folding. Also, you don't have a lot of implieds to get called by a lower flush on the river should you hit.

I agree that you should 3barrel if you're planning to cbet because you have the backdoor flushdraw, but that doesn't mean it's the optimal play.

Also, I agree that if he had a draw he would probably raise (there aren't a lot of draws in his range to begin with), but ruling out sets out of his flatting range is a big step in the dark IMO.