AA with action from UTG, help needed

[brer]

I have ~350 in chips, villian has ~175. It is a NLHE ring game at a Vegas casino, 1-2 $200 max.

Villian raises UTG to $20, I raise from MP to $60 with AA. Villian thinks for some time, then asks me to show one card for $5, which I refuse, and finally calls the bet, putting $120 in the pot before the flop, leaving Villian with ~$115.

If the villian checks, should I be pushing just about any flop in this situation?