As I see it you shoved and not villain... Im not very happy with it but Im probably going with the hand as you did. He could do this with AxKh,AxQh,A3 which you beat.. vs made flushes you have @28% eq.

Vs something like TT,33,AdTd,AsTs,Ad3d,As3s,AdKh,AsKh,AdQh,AsQh,AdTs,AdTc,AsTd,AsTc,Ad3s,Ad3c,As3d,As3c (presuming AA are 3b PF)

you`d be at 56,6% .

I don't know if I like just calling, I don't think it's bad but we`ll have to be ready to get rid of the hand if he fires on another heart... you probably won't get that much action from Ax on a doubled T either.

I would just call the flop. As played I don't like it but I don't think we can do anything else than jamming.

Call flop cbet, AT isn't strong enough to gii vs a super wide range which contains insane ammount of flushes and sets. You got position use it

I don't like raising here at all - I think that we do not have a significant equity advantage vs his BC range, so I would just call.

I actually don't mind raising the flop, but you should definitely make it smaller, like no more than 1.20. You do get value vs. some Ax with one heart, Khx, random pairs with a high heart, and protection vs. air with one heart that won't barrel is very good. Once you get 3bet you could possibly make an exploitative fold, because a lot of people at small/micro stakes only have nutted hands for 3betting monotone boards (set or flush), but a more "solid" play would be to call. 4betting flop is a mistake because you don't want to get it in. But just because you don't want to get it in in a certain spot doesn't necessarily mean you can't initially value raise.