NL50 150BB's deep w/AA. How musch to 4 bet PF?

[JROK777]

Full Tilt Poker
No Limit Holdem Ring game
Blinds: $0.25/$0.50
6 players
Converter

Stack sizes:
Hero: $82.30
UTG+1: $48.75
CO: $50
Button: $38.65
SB: $85.15
BB: $86.30

Pre-flop: (6 players) Hero is UTG with A[img]/images/graemlins/heart.gif[/img] A[img]/images/graemlins/diamond.gif[/img]
<font color="#cc0000">Hero raises to $1.75</font>, 2 folds, <font color="#cc0000">SB raises to $5.75</font>, BB folds, <font color="#cc0000">Hero raises to $22.25</font>, <font color="#cc0000">SB raises all-in $85.15</font>, <font color="#cc0000">Hero calls all-in $61.8</font>.
Uncalled bets: $1.1 returned to SB.

Villian is solid and is probably a 2p2er. We are too deep to just call his reraise. I had a hard time choosing how much to 4 bet him to. What amount is correct and why.