With the Q on board, your Jacks may be no good. Its cheaper to find out early, (although this hand is an exception with the river J).
Bet the flop; if raised reraise. If he still calls the reraise you are toast.
Alternately, raise his bet on the turn. If he calls hes got a hand. Play accordingly, as in limp it home as cheaply as possible, or just fold to a large bet.