I don't hate this board. If the board has to have a KQJ on it, then I'm glad for the paired jacks because you're ahead of KQ. I don't put him on KK/QQ like ever, so I'm only worried about Jx and AT and T9. I think he has a random K and/or Q that will pay off more often than he has those hands.

So I would check/call the flop (standard for me with the paired board) and then bet the turn. When he bets the flop, I'm thinking most of the time he does not have a J because most folks slowplay trips. And I don't want him to see a free river card when I have no clue about his hand -- any K Q or 9 would give me a very unpleasant river decision. (Also I'm pathologically unable to reraise preflop and then check/call the flop and the turn not knowing where I stand.)