20/40 4 handed - good move or spew? (part2)

[Fortitude]

I've been acting on my reads a little more aggressively these days and Im trying to make sure I'm not going over the top so here is part 2:

30 hands or so with SB, he's done some donkish things but his pre flop standards are okay. 50 hands or so with BB, he is a little aggro but also has respectable pre flop standards.

20/40 4 handed

I open on button with KTs, SB 3 bets, BB calls, I call.

flop: jd2s8d

SB checks!!, BB checks, I bet, SB folds!!, BB raises, I call.

BB's raise doesn't make any sense to me, the pre flop raiser already checked and gave up the lead so if BB had a hand he wanted to bet he would have bet it instead of checking to me and giving us all very dangerous free cards.

turn: 2s

BB bets, I raise

Maybe I would have been better off 3 betting the flop and betting the turn? Thoughts?