Was this the correct play?

PokerStars No-Limit Hold'em, $0.25 BB (7 handed) from (Format: FlopTurnRiver)

MP2 ($25.75)
CO ($37.85)
Button ($39.65)
SB ($24.15)
BB ($26)
Hero ($43.95)
MP1 ($36.90)

Preflop: Hero is UTG with K, K.
Hero raises to $1, 2 folds, CO calls $1, Button calls $1, SB calls $0.90, 1 fold.

Flop: ($4.25) J, Q, 4 (4 players)
SB checks, Hero bets $3, CO calls $3, Button calls $3, SB folds.

Turn: ($13.25) A (3 players)
Hero checks, CO checks, Button bets $7.5, Hero calls $7.50, CO folds.

River: ($28.25) 6 (2 players)
Hero checks, Button bets $13.5, Hero folds.

Final Pot: $41.75

Results in white below:
Button doesn't show.
Outcome: Button wins $41.75.

Bet more on the flop, and if you're going to call a turn bet you may aswell lead out again.

Check-raise all in on turn not good?
If i lead out and he goes all in?