Beautiful flop for you.

I don't know if I would push on the flop though. What is he going to call with that doesn't beat you? What he had is one of the few hands that he might call with. Most hands he would call with like two hearts or a set or top two pair have you beaten pretty well.

I would just call the bet on the flop. I am drawing to the nuts and right on the flop I may have the best hand anyway. By just calling the pretty weak bet you get a cheap card to draw at the nuts and you encourage him to bluff at you on the turn if he doesn't in fact have a hand because he thinks you're on a draw (which you are but you also have tptk). And if he does have a hand you are saving your money while getting a cheap look at a card to draw out. And if he is betting a K or J flush draw you are also not shutting him out of the pot and losing the money you'll make when the last heart comes.

But I don't think pushing on the flop is necessarily a bad one, just not the optimal one imo.

Edit: Whoops, I thought you had said he bet out 2xBB on the flop, not 2x pot. In that case, ignore what I wrote, that is advice for when he makes a weak bet at the pot. When he makes the bet he did I think you have to push or fold depending on what if any read you have on him. Probably the only time I fold this is if I know the guy to be a rock. Otherwise I push and hope he a) folds b) is protecting a hand like KhQx or c) gets drawn out on by ME!