I think this is the wrong board to check behind on. There are simply too many hands that you presently beat that have 6 (overs to 8), 9 (all fd), (11/12 fd + 1 over) and even 15 (fd + 2 overs) outs against you. Forgive me if I get a number or two wong above. His outs are plenty anyway.
Ideally, you want sort of a way ahead/way behind situation, or a picked up draw (on turn) with a weak hand when you think you are behind, to check behind. If he likes to bluff river if the turn gets checked, then you have an added bonus.
See also this thread: Checking Behind on the Turn
Edit: Suppose you have Q :spade:Q
on a A :diamond:K :club:2 :spade:7
board in a 3-bet pot. Now he either has you beat, or has at most 5 outs to beat you. In addition, you block many high straights. With this board, a check behind is at least a decent candidate.
More edit: Another candidate: T :diamond:9
on a 7 :spade:K :diamond:A
6
board in 2-bet pot. I'd sometimes like to take a free card here.
/Johan =