Q52, I definitely continue here with JJ. I'm getting value from anyone who's going to peel - 34s, A3, A4, AK, KJ might peel, TT, 99, 88, 77, 66. If the board is double suited you can add pretty much all of the Ax Kx range. A5, 65, A2.
A lot of hands will call a bet that are way behind JJ here. Your only scary hands are AA, KK, AQ, KQ, QJ (which there's not many of), Q10. Maybe Q9s.
SO, I call this a value bet. Re-evaluate on the turn.
Also, it protects against hands like A9, AT, AJ, KT, just because they'll usually fold out.
Now, if you a turn a King, it's much harder to figure out what to do.