[aliensyndm]

No reason to believe your AA isn't good ? Erm what about the check raise ?
A check raise normally screams I HAVE A MONSTER HAND.
It does depend on the player but normally when someone check-raises you they have better than 1 pair. I don't wanna be working out my chances to outdraw him. Sure if you go all in you've still a reasonable chance of outdrawing him if you are beaten but most of the time you are only gonna be called when you are behind, why do that ? How much of the time are you gonna be called all in when are you actually winning ? Assuming your opponent isn't a total numpty not very often. Like I said before I wanna be pretty certain I have the best hand if I am gonna commit my whole stack, having just been check-raised, normally the indication of a very strong hand, I cannot be certain that I do.

By your logic if you believed your aces were good on the flop and hence were willing to go all in there's no reason at all not to call a pot sized bet on the turn if it falls a blank then surely ? Obviosuly now after the turn your chances of hitting the flush are reduced but if you think your aces are good anyway it doesn't matter. The problem on the turn is, what if your aces aren't good ? That's the decision right. Well why stick all your chips in on the flop when they might not be ? For $10 you have a chance to be certain they are.
You can then get some further info on whether they are good or not by the players action on the turn. If he checks you can check too. If it's another pot sized bet you then that's some more information on the how good your aces are. The main drawback to just calling the $10 is you may end up folding the best hand. That's the key thing you obviously want to try and avoid. But by calling the $10 you have two plays from your opponent to give you an idea of how good you are, by going all in on the flop you only have the inital check raise to go on. Plus you are only likely to be called when you are behind.

Opponent does come into it a bit I would say. Against a loose aggressive person putting him all in is probably not too bad of a play. He may think seeing as you bet $10 to a $13.50 it was a sign of weakness and try and get you off it. Against a tighter player I would be far more wary of a check raise.