Guy calls you on a jack high, rainbow flop; turn pairs the jack & you don't have one yourself. What you know:

1. he's probably (50% likely) got a jack, unless he's on a straight draw or is a loose player with middle pair.
2. on the off chance he has JT, JA, or J9 your draw is compromised anyway.

Check/fold the turn. Don't bet it, definitely don't call a big bet or raise from him at that point.