NL 100 Full Ring

[Padster]

Sorry I dont have the hand history but the details are as follows...

Full ring $100. My image solid possibly a little agg. I am UTG+1 AA and limp. $200 stack. Short stack mid shoves for $13 following a beat the previous hand for virtually his stack. Late position Villain calls (solid from what I've seen, $150 stack). Not sure if this is important but he's had some needle with the short stack, although he wasnt the one who delivered the beat the previous hand.

I raise to $40. Not sure if table had noticed but I hadn't limp raised in the session before (been there an hour). Villain calls.

So pot $95. Flop KKQ rainbow.


I bet $50. Villain calls $50 out of his remaining $110 stack. Turn 2.

I check Villain shoves.

My question is twofold :

1) How was the flop play? Bet too big (obviously AA)? Does a smaller bet invite a steal or simply get the job done cheaper?

2) Given there's a short stack so the hand will go to showdown (so I will see the bluff if it is one) is there any way I don't fold? Or is folding weak? Is a $60 call for a pot of $250 worth calling down a bluff (as surely a bluff's all I'm beating)?