10NL - Axs in SB hits Ace, how do you play these?

[akak]

Guy was something like 74/26/3 after ~250 hands. Loves to to play a lot of hands cheaply, and is otherwise a decent player.

Ultimate Bet No-Limit Hold'em, $.10 BB (6 handed) Hand History converter Courtesy of PokerZion.com

UTG ($4.52)
MP ($11.57)
CO ($12.05)
Button ($4.15)
Hero ($9.90)
BB ($12.63)

Preflop: Hero is SB with 6[img]/images/graemlins/spade.gif[/img], A[img]/images/graemlins/spade.gif[/img].
<font color="#666666">3 folds</font>, Button calls $0.10, Hero completes, BB checks.

Flop: ($0.30) J[img]/images/graemlins/heart.gif[/img], A[img]/images/graemlins/diamond.gif[/img], 2[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(3 players)</font>
Hero checks, <font color="#CC3333">BB bets $0.3</font>, Button folds, Hero calls $0.30.

Turn: ($0.90) K[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(2 players)</font>
Hero checks, <font color="#CC3333">BB bets $0.9</font>, Hero calls $0.90.

River: ($2.70) 7[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players)</font>
Hero checks, <font color="#CC3333">BB bets $1</font>, Hero calls $1.

Final Pot: $4.70

I know my line was probably horrendous here, and I'm having trouble playing these Axs in the SB.

I don't want to lead out on the flop since generally, the only hands that will call are better aces. At the same time, if I don't I run into situations like these.

How do you guys play in this situation?