50NL KK runs into a horrible board

[beavens]

villian is 51/19/.76 over 61 hands

Party Poker No-Limit Hold'em, $ Hero (6 max, 4 handed) FTR converter on zerodivide.cx

UTG ($33.02)
Button ($141.55)
SB ($110.80)
Hero ($101)

Preflop: Hero is BB with K[img]/images/graemlins/diamond.gif[/img], K[img]/images/graemlins/heart.gif[/img]. SB posts a blind of $0.25.
<font color="#666666">2 folds</font>, <font color="#CC3333">SB (poster) raises to $1</font>, <font color="#CC3333">Hero raises to $7</font>, SB calls $6.

Flop: ($14) 4[img]/images/graemlins/spade.gif[/img], 5[img]/images/graemlins/diamond.gif[/img], 2[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(2 players)</font>
SB checks, <font color="#CC3333">Hero bets $10</font>, SB calls $10.

Turn: ($34) 3[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players)</font>
SB checks, Hero checks.

River: ($34) 4[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">SB bets $40</font>, Hero ???.

at the time i figured i was probably going up against Ax.

what would you guys do here?

flop bet too small with a draw heavy board?

did checking the turn lose this hand for me?

i really hated how this hand turned out.