100NL : AA avoid paying off a set + weird action

[cbloom]

Party Poker No-Limit Hold'em, $ BB (10 handed) internettexasholdem.com

UTG+2 ($168.05)
MP1 ($84.50)
MP2 ($98.80)
MP3 ($47.37)
CO ($44)
Button ($96)
SB ($101.25)
BB ($111.40)
Hero ($94.85)
UTG+1 ($248.85)

Preflop: Hero is UTG with A[img]/images/graemlins/diamond.gif[/img], A[img]/images/graemlins/spade.gif[/img]. SB posts a blind of $0.50.
<font color="#CC3333">Hero raises to $4</font>, UTG+1 calls $4, <font color="#666666">1 fold</font>, MP1 calls $4, <font color="#666666">4 folds</font>, SB (poster) calls $3.50, <font color="#666666">1 fold</font>.

Flop: ($17) 6[img]/images/graemlins/diamond.gif[/img], 4[img]/images/graemlins/spade.gif[/img], 5[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(4 players)</font>
<font color="#CC3333">SB bets $1</font>, <font color="#CC3333">Hero raises to $12</font>, UTG+1 folds, MP1 calls $12, SB calls $11.

Turn: ($53) 2[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(3 players)</font>
<font color="#CC3333">SB bets $1</font>, <font color="#CC3333">Hero raises to $20</font>, MP1 calls $20, SB calls $19.

River: ($113) K[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(3 players)</font>
<font color="#CC3333">SB bets $20</font>, Hero calls $20, MP1 calls $20.

Final Pot: $173

Results in white below: <font color="#FFFFFF">
SB has 7d Jd (flush, king high).
Hero has Ad As (one pair, aces).
MP1 has 5d 5c (three of a kind, fives).
Outcome: SB wins $173. </font>

Ok, so I screwed up on the river here, it's pretty clear I'm beat at that point. "SB" is making it obvious he's on a draw. When MP1 calls my bet on the turn it's pretty clear he must have a set. Is there a better way to play the turn to avoid losing that extra $20 ?

I hate paying off sets with overpairs, it feels like a leak. I make my money from hitting sets and cracking overpairs, I don't want to just give it back when the roles are reversed.