QJs OOP, check/raise on paired flop

Hello guys.
I am back with another trouble hand.
OTF: think I could cbet OTF, but check is fine too imo. But his cbet was a quite big, but I dont see any reason for betting trips with such a big sizing. Decided to check/raise, cause I expect that he is stabbing a ton.

OTT: Hit a gutter and continue, because I want to make him fold his 55-88, weak FDs,4x hands.

OTR: Firstly I wanted to just check, but then was some voice in my head, that I have blocker on KQ,KJ and he has a lot of busted FDs and the button calling range is mainly from suited kings probably KJs-K8s + some sets (not that many combos), but still if he is able to fold his busted 9x and 7x FDs, then it should be profitable to bet here.

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

Hero (CO): 113.7 BB
BTN: 220.1 BB (VPIP: 32.83, PFR: 17.76, 3Bet Preflop: 8.67, Hands: 954)
SB: 100 BB (VPIP: 26.68, PFR: 19.23, 3Bet Preflop: 10.43, Hands: 999)
BB: 50 BB (VPIP: 23.86, PFR: 16.43, 3Bet Preflop: 8.14, Hands: 920)
UTG: 120.5 BB (VPIP: 30.16, PFR: 18.82, 3Bet Preflop: 7.71, Hands: 1,063)
MP: 102.8 BB (VPIP: 23.59, PFR: 17.35, 3Bet Preflop: 5.06, Hands: 1,182)

SB posts SB 0.5 BB, BB posts BB 1 BB

Pre Flop: (pot: 1.5 BB) Hero has J♠ Q♠

fold, fold, Hero raises to 2.5 BB, BTN calls 2.5 BB, fold, fold

Flop: (6.5 BB, 2 players) K♦ K♣ 4♣
Hero checks, BTN bets 6 BB, Hero raises to 16 BB, BTN calls 10 BB

Turn: (38.5 BB, 2 players) 9♠
Hero bets 24.4 BB, BTN calls 24.4 BB

River: (87.3 BB, 2 players) 7♥
Hero bets 70.8 BB and is all-in, BTN calls 70.8 BB