[excession]

I'm a little confused - saying the AQs player should see a flop when is getting 2:1 on his money is one thing, but to somehow claim that AQs is a better hand here is so counter-intuitive it needs a lot stronger justification than you are showing.

The JJ player not only has position, he has the lead. If AQs player is known to be so weak tight as to not often bet out unless he hits (and the JJ player know this) then a bet from the AQs player may elicit a fold (assuming overcards to JJ on flop and no J). But 2/3 of the time AQs player won't hit, he'll check and lose the pot.

Otherwise with the lead the JJ player is likely going to play back at the AQs no matter what (or he sets the precedent that the lead can be stolen from him in a raised pot by an OOP bet).

Certainly just a Q hitting on the flop is unlikely to scare an aggro JJ player off. And when the flop comes Q, 8, 7 rainbow, AQs bets 2/3 pot and gets raised back what exactly is he going to do? The re-raise pre-flop from most players indicates AA, KK, QQ or sometimes JJ or AK. Even if he calls the raise, if turn is a blank and AQs guys slows down and faces another pot sized bet surely he has to lay down?

Similarly if the JJ player has the balls to raise into an ace flop - how can the AQs player think anything but 'uh oh' AK (or AA)?

As several posters have pointed out, if a Jack falls with either an A or Q (or better both) on the board the AQs player is in a whole heap of deep stack trouble.

AQs (at least without TP + nut flush draw) is simply a horrible trappy hand to be trying to play OOP into an aggressive pre-flop re-raiser unless you are really sure that he is full of it..now if this was a battle of the Button and the BB or a 3 handed table maybe I could see it -but I'm assuming this isn't the case and we are at either 6 max or full ring..