I seriously doubt that anyone who played JJ that way heads up would fold at that point.
If I bet the flop and he raises I pretty much have to fold. My plan was actually to check / fold if he bet, but once he over bet the pot, I didnt believe for a second that he had an ace.
I check raised all in and he called with
[3d] and missed. I really thought he had a middle pair though based on the obvious attempt to get me to laydown to the flopped ace.
If he bet $30 I wouldve folded. If he hit the bet pot button I most likely wouldve folded. $50 is just too obvious that he doesnt have an ace and knows that I dont either since I checked.