[Lurker4]

I like calling turn + river over raising turn; button is out so hand protection is not as important, you may get 3-bet when you have 5-7+ outs, so folding to the 3-bet is no good, but putting 3 bets in on the turn on this board is definitely not favorable against BB's range. You are in position, so you can assure that a river bet goes in if BB is on KJ/worse Kx/pair + spade. Lastly, if BB is semibluffing spades he may bluff bet river if he misses on this scary board, hoping you'll fold something.