I'm definitely betting that flop. Assuming your jacks are outs, which they aren't but you can't really know that yet, you are actually a favorite to win the hand over any pair below JJ so this flop is definitely allinable. Your limp raise pre-flop and then check/call on the flop looks like AK to your opponent. I would have bet about 2/3 the pot on the flop and when he raised you would pretty much know what his holding was and you could either move AI or fold at this point.