Do I check or bet this river?!?! Please help.

[checkit888]

30/60 party

Everyone folds to me. I'm on the button with [ Kd 9c ]
I raise, sb and bb call

** Dealing Flop ** [ Th, Jd, Qs ]
I bet, SB raises, BB call, I call

** Dealing Turn ** [ 2h ]
SB bets, BB call, I raise, SB 3bet, BB calls, I cap

** Dealing River ** [ Qh ]
SB checks, BB checks,

I what? Check or bet? I'm thinking SB has at minimum 2 pairs, a set, or smaller straight. Not sure what the heck BB is doing calling the turn. With a paired board and flush draw on the river, can I just check the river?

Thanks