Did I miss value here?

[JoostR]

Poker Stars, $0.01/$0.02 NL Hold'em Cash Game, 6 Players
LegoPoker Hand History Converter

SB: $2.99
BB: $2.37
UTG: $1.66
MP: $5.47
CO: $7.94
Hero (BTN): $6.68

Pre-Flop: A[img]/images/graemlins/heart.gif[/img] A[img]/images/graemlins/spade.gif[/img] dealt to Hero (BTN)
2 folds, <font color="red">Hero raises to $0.20</font>, 2 folds, MP calls $0.14

Flop: ($0.31) K[img]/images/graemlins/diamond.gif[/img] 4[img]/images/graemlins/diamond.gif[/img] 2[img]/images/graemlins/heart.gif[/img] (2 Players)
MP checks, <font color="red">Hero bets $0.25</font>, MP calls $0.25

Turn: ($0.81) 8[img]/images/graemlins/heart.gif[/img] (2 Players)
MP checks, <font color="red">Hero bets $0.60</font>, MP calls $0.60

River: ($2.01) K[img]/images/graemlins/spade.gif[/img] (2 Players)
MP checks, Hero checks

Results: $2.01 Pot ($0.10 Rake)
MP showed J[img]/images/graemlins/diamond.gif[/img] Q[img]/images/graemlins/diamond.gif[/img] (a pair of Kings) and LOST (-$0.99 NET)
Hero showed A[img]/images/graemlins/heart.gif[/img] A[img]/images/graemlins/spade.gif[/img] (two pair, Aces and Kings) and WON $2.03 (+$1.04 NET)

I was scared of the second king but in retrospect he was problably on a flush draw. Should i have bet the river here for value or did my check make sure i wasn't at risk of being check-raised by trip kings? I think a flush draw wouldnt call me anyway so what hand would call me that i can beat right?

- edit: the hand history wasnt exactly right. MP raised to 0.06 and i raised him.