I don't think there's really room for a check-raise here, nor do I think it would have accomplished anything for you.

FLOP -- he's likely checking behind you; if he bets and you raise, I don't see him folding an open-ended straight draw to a 6.5BB pot for one bet
TURN -- he obviously loves a check-raise and will raise you, at which point you're obliged to give up the hand, having saved yourself no bets over how you actually played it
RIVER -- see turn

I think you played it right. With the way BB played it, you had no cueing that would have allowed you to get away from this. I think Villain played it well also... probably gained at least one bet out of calling vice raising the turn.