Preflop going bigger would be good, but once you get min-3bet you can’t fold anything.

The flop, I don’t like. You have no backdoors, one overcard and a gutshot and not even all of those are 100% live, and you’re up against what is probably a strong range of hands. I think this is pretty button-clicky and unnecessary to call here with so little equity on a dynamic flop. If you’re doing this kind of thing frequently, especially in 3-bet pots, you’re probably giving away a lot of chips.

As played, I think check-folding, check-raising, and betting river are all better lines than check-calling so I hope you didn’t do that. If you think villain is capable of bet-folding the Th or even the Kh then check-raising is great, since most of villain’s Ah combos are likely to bet turn while we can still have a bunch of AhJx combos and some others too, and thus villain is pretty capped and might even fold 100% of his range to a check-raise if he always bets the Kh or Ah on turn.

If you think villain never folds a decent heart to any significant action then check-folding is better, but betting out is probably the line I like the most. And not betting for ‘value/blocker’ either – there’s no value here, we get called by worse exactly 0%. I’m betting as a bluff, quite big, to put pressure on hands like non-heart AA/KK which might check the turn, non-heart TT/99, non-heart AQ…basically anything without a heart is folding river most likely, and since most of villain’s Ah/Kh combos are betting turn, I think we get a lot of folds.