Was I correct to check the flop and turn? I guess value here is: Small aces, 77, and flushes. But I also think considering I checked both the flop and the turn he could be turning a lot of hands into a bluff. I ended up calling because I figured kings is the best hand I will ever have that I check both flop and turn, so if I was to fold I would be folding my entire range that I have played this way.

PokerStars - $0.10 NL FAST (6 max) - Holdem - 6 players
Hand converted by PokerTracker 4

BTN: 100 BB (VPIP: 16.67, PFR: 0.00, 3Bet Preflop: 0.00, Hands: 7)
SB: 105.7 BB (VPIP: 21.09, PFR: 12.50, 3Bet Preflop: 3.28, Hands: 130)
Hero (BB): 108.5 BB
UTG: 140.6 BB
MP: 174.4 BB (VPIP: 12.76, PFR: 11.73, 3Bet Preflop: 3.61, Hands: 203)
CO: 99.5 BB (VPIP: 24.32, PFR: 10.81, 3Bet Preflop: 16.67, Hands: 39)

SB posts SB 0.5 BB, Hero posts BB 1 BB

Pre Flop: (pot: 1.5 BB) Hero has K K

fold, fold, fold, BTN raises to 3 BB, fold, Hero raises to 9.5 BB, BTN calls 6.5 BB

Flop: (19.5 BB, 2 players) A Q A
Hero checks, BTN checks

Turn: (19.5 BB, 2 players) 7
Hero checks, BTN bets 10 BB, Hero calls 10 BB

River: (39.5 BB, 2 players) 3
Hero checks, BTN bets 30 BB ???

i think we could lead turn 10bb and than blockingbet river 16bb to fold to a raise. the way you played cannot let us to make him a range and you will call without info..

Fold river without much thought. Turn probably trash cans us already a lot but wouldn’t bring myself to fold there. You’re levelling yourself if you calll river

I think checking flop and turn both are fine. And the x/c on the turn is fine too. WP if you folded river. QJ/QT are probably the only hands that bluff here. Maybe could call with Kh I guess, but probably see Ax here quite a bit.

Vs 30 BB sizing on the river you would most probably see flushes, full houses and Qx but you would rarely see Ax. You block a bit of their bluffing range as well so this is an easy river fold