Re: how bad was this?
It depends on your read on BB, but a lot of people with BBs stats are donking KTs or QJ or even A8s here (which includes the fact that they call preflop in the BB facing a 3-bet).
You need a strong read that the BB will bet out a lot of draws and check/call or check/raise most pairs because there are a lot more 1-pair or better hands than they are decent draws out there. When the turn brings an ace, most of his drawing "got there" (in the sense of outdrawing you as even AT and AJ now beat you). So check the turn and fold the river UI.
You don't say which two flop cards are hearts, but keep in mind that if villain is on a flush draw, he most likely has one of the A,K or Q of hearts -- enough to beat you already. (Or JhTh which has you crushed.)
In the best of scenarios, your aggressive play in this hand could have been marginally +EV. More likely, though, it was significantly -EV.
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