5nl KK flops an Axx board. How is this line?

[Bubbagump]

No reads on villain.

PokerStars No-Limit Hold'em, $0.05 BB (8 handed) Poker Stars Converter Tool from FlopTurnRiver.com (Format: 2+2 Forums)

saw flop|<font color="#C00000">saw showdown</font>

BB ($4.39)
UTG ($10.12)
UTG+1 ($5.35)
MP1 ($5.28)
MP2 ($4.25)
<font color="#C00000">Hero ($6.18)</font>
Button ($2.62)
<font color="#C00000">SB ($6.38)</font>

Preflop: Hero is CO with K[img]/images/graemlins/heart.gif[/img], K[img]/images/graemlins/diamond.gif[/img].
<font color="#666666">1 fold</font>, UTG+1 calls $0.05, <font color="#666666">2 folds</font>, <font color="#CC3333">Hero raises to $0.25</font>, <font color="#666666">1 fold</font>, SB calls $0.23, <font color="#666666">1 fold</font>, UTG+1 folds.

Flop: ($0.60) 5[img]/images/graemlins/heart.gif[/img], Q[img]/images/graemlins/diamond.gif[/img], A[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(2 players)</font>
SB checks, Hero checks.

My thinking here is if I bet, I only fold the hands that I am ahead of and throwing away money if villain has an Ace.

Turn: ($0.60) 2[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">SB bets $0.3</font>, Hero calls $0.30.

Villains weak bet here does not necessarily mean I am behind so I call hoping for a free show down.

River: ($1.20) A[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">SB bets $0.6</font>, Hero calls $0.60.

Final Pot: $2.40


There is a thread in the archive section about playing KK with an Axx flop and most posters were in agreement that the best line was to check flop check turn and fold to a river bet. But given the bet size, is a call in this spot warranted?