I would check and take the free card. If another overcard like a king or ace comes out, then you can probably lay JJ down on the river if he bets. If a blank hits, then checking will let you show down for only one bet. If he check raises you again on the turn, then he's representing something that's at least as good as a pair of queens. So you would probably want to fold the jacks there anyways. So in both scenarios, you lose a bet at worse, but by checking on the turn you can gain some information on your opponent by making him show his hand. Also, there's the possibility that he checks