Overall, seems from BB's play that he thinks you are stealing and c-betting. Or has a monster...

Pre-flop, standard steal situation and your hand is good enough for that - although I would often fold here this early on, the blinds aren't really worth stealing yet. Play super-tight early and get LAG later...

Flop. I like it, but am scared by the BB check-call - from here on in I want to see the river cheaply.

Turn. Dunno, calling is fine, raising is maybe - I don't think I fold here.

River, I like that you checked behind. I wouldn't be that surprised to see KTen here, but AJ and other hands that beat you are likely enough too.