[Brom]

Like I mentioned, without a read there is no reason to believe this is AA. Against an unknown opponent I think your play is default.

Would I cap in his shoes? Well I did say something along the lines of 3-betting (in your shoes) and folding to a cap. This was because I couldn't see your hand being good enough of the time when there are four bets going in. For this same reason I don't think I'd cap in his situation. Sure you can now beat the JJ but all those other hands are still going to be there too much of the time that he's in for that 4th bet. If he was truly terrible though and I was certain he'd pay off with hands like two pair most of the time, then I'd be hard pressed not to cap it - even if only for the future.