Overpar+flushdraw in 3bet pot. Did I overplay turn?

Posted 6 years ago

Blinds: $0.01/$0.02 (6 Players) BN: $4.19 (Hero)
SB: $2.76
BB: $2.11
UTG: $2.21
MP: $2.39
CO: $1.90

Preflop ($0.03) Hero is BN with 4 K K A

UTG raises to $0.04, MP folds, CO calls $0.04, Hero raises to $0.19, 2 folds, UTG calls $0.15, CO folds

Flop ($0.45) 6 T 2

UTG checks, Hero bets $0.44, UTG calls $0.44

Turn ($1.33) 6 T 2 4

UTG checks, Hero bets $1.29, UTG raises to $1.58 and is all in, Hero calls $0.29

River ($4.49) 6 T 2 4 5

Final Pot BN wins and shows a flush, Ace high.
UTG lost and shows three of a kind, Sixes.
BN wins $4.34
Rake is $0.15

I'm not sure if I should have checked the turn instead. What do you guys think?