I am check-calling this river. Its possible he flopped a straight draw and called down, but he would fold that to a bet. You are splitting if he has a king. If he called down with bottom pair on the flop, you're screwed of course. So the only time you collect is when he is holding a jack. Now that I said all that, I bet-fold. I think check-folding is weak..And he is not going to bet that jack often on that board.