SSH Flop Quiz #16 -- AJs (crossposted)

[aK13]

You are in a loose and very aggressive game. You have A[img]/images/graemlins/spade.gif[/img] J[img]/images/graemlins/spade.gif[/img] in the big blind. Four players, including the SB limp. You raise. Two limpers call, and then the button (limp)-reraises. The small blind calls and you cap. Everyone calls (20 small bets). The flop is K[img]/images/graemlins/heart.gif[/img] Q[img]/images/graemlins/club.gif[/img] 7[img]/images/graemlins/spade.gif[/img], giving you a gutshot, and overcard, and a backdoor flush draw. The small blind checks, and you bet.

This bet is very unlikely to pick up the pot right now, And we're basically not folding out any hands that we would like to fold, so the only other reason to bet right now would be for value. How much value does our gutshot + BDFD have here against this field? Is it really enough to justify a bet here?