AA gets 4-bet pre-flop, flat call or shove? 100bb deep

[LoLoTrickyU]

Villain is 20/14/2.0

Full Tilt Poker - No Limit Hold'em Cash Game - $1/$2 Blinds - 5 Players - (LegoPoker Hand History Converter)

SB: $99.40
BB: $232.10
UTG: $190.40
Hero (CO): $197.00
BTN: $161.50

Preflop: Hero is dealt A[img]/images/graemlins/diamond.gif[/img] A[img]/images/graemlins/club.gif[/img] (5 Players)
<font color="red">UTG raises to $7.00</font>, <font color="red">Hero raises to $27.00</font>, 3 folds, <font color="red">UTG raises to $65.00</font>, <font color="red">Hero raises all-in to $197.00</font>, UTG folds
Uncalled bet of $132.00 returned to Hero

Pot Size: $133.00

I opted to shove here but really think I made villain fold KK here. Villain put in $65 out of his $200 stack preflop and folded. Should I have just flat called and gotten our stacks in on the flop or just shove like I did? Thx. Gl.