NL10- KK on A high board, thoughts on turn line please.

[youngmachetes]

Poker Stars - No Limit Hold'em Cash Game - $0.05/$0.10 Blinds - 3 Players - (LegoPoker Hand History Converter)

Hero (SB): $9.20
BB: $25.60
BTN: $49.75

Preflop: Hero is dealt K[img]/images/graemlins/heart.gif[/img] K[img]/images/graemlins/diamond.gif[/img] (3 Players)
BTN folds, <font color="red">Hero raises to $0.40</font>, BB calls $0.30

Flop: ($0.80) A[img]/images/graemlins/diamond.gif[/img] 3[img]/images/graemlins/diamond.gif[/img] J[img]/images/graemlins/club.gif[/img] (2 Players)
Hero checks, BB checks

Turn: ($0.80) 4[img]/images/graemlins/diamond.gif[/img] (2 Players)
<font color="red">Hero bets $0.60</font>, BB calls $0.60

River: ($2) 3[img]/images/graemlins/heart.gif[/img] (2 Players)
Hero checks, BB checks

Pot Size: $2.00 ($2 Rake)

BB had 3[img]/images/graemlins/spade.gif[/img] 2[img]/images/graemlins/spade.gif[/img] (three of a kind, Threes) and LOST (-$1.00)
Hero had K[img]/images/graemlins/heart.gif[/img] K[img]/images/graemlins/diamond.gif[/img] (two pair, Kings and Threes) and LOST (-$1.00)


villain is a mega fish. i left results in because they're funny, and don't really have much to do with what i'm asking. did i take an okay turn line? it was a valuebet fwiw...he's def. calling with some worse flush draws and other weaker made hands, and his flop check leads me to believe i have the best hand.