I don't see what hands you have beat here unless he really liked the look of those Jacks. As was already said, it's a fold/shove situation. The flop check leads me to believe he's got Kings and if you bet your remaining stack you might get him to fold them, though there's always the chance he flopped trip Aces and you're done either way.

You can't beat any hands that the average person is 4-betting with, so your options are to fold or try and bluff him out of the pot. As this is 2NL, we can't even reliably say that the guy will fold his Kings. As played I fold the turn.

Toughie.