Huh.
I am having the most trouble figuring out what the BB is calling the turn with that he checks the flop with. And if it was a missed checkraise, why doesn't he do it on the turn. The only thing I can figure is that he hits 2 pair on the turn (with 10-8) but is fearful of the straight and flush. So he calls, 3 bets? Confusing. Maybe he has the King of hearts...
I'm thinking a bet on the flop would be good. To see where you are at. Might've made the rest of the hand a bit easier...