$22 PP - Hooks with an A on the flop and again on the turn

[playtitleist]

I am convinced I f'd this one up.

As added thought, what about the fact that he DID NOT push the flop? I think he pushes any ace with his stack. Then, as said before, when the 2nd Ace came he was pretty confident I didn't have one, so he was free to push his 9 or PP or whatever he has made. Can a $22er hold back from pushing this flop with an Ace (or a set) with this chip stack?