I mae a mistake checking this flop but should I have been able to let this go on the turn? Villians stats were 60/4/1.5. I really didn't put him on KK, even w/ his stats I thought he'd raise pf so I figured he had AK or QQ.. Boy was I wrong..

PokerStars No-Limit Hold'em, $0.05 BB (6 handed) from (Format: FlopTurnRiver Cards)

SB ($9.95)
Hero ($13.66)
UTG ($9.44)
MP ($11.01)
CO ($7.10)
Button =#A500AF(Villian)/ ($9.68)

Preflop: Hero is BB with , .
2 folds, CO raises to $0.2, Button =#A500AF(Villian)/ calls $0.20, 1 fold, Hero calls $0.15.

Flop: ($0.62) , , (3 players)
Hero checks, CO checks, Villian checks.

Turn: ($0.62) (3 players)
Hero bets $0.45, CO folds, Villian raises to $0.9, Hero raises to $2.3, Villian raises to $3.7, Hero raises to $8.95, Villian raises to $12.28, Hero calls $2.38.

River: ($24.23) (2 players)

Final Pot: $24.23

Results in white below:
Hero has 7d 7c (full house, sevens full of jacks).
Villian has Kc Kh (full house, kings full of jacks).
Outcome: Villian wins $24.23.

Stack off here every time vs that villain.

YEP, your play was fine. would stack off here 100% of time

Lead into the raiser. Whenever I spike a set on the flop, I ALWAYS lead into the PFR (if its a raised pot). There is nothing you can do there. Just make sure you always play your sets fast in raised pots.