1) How would you play this hand?
2) I wasn't really sure about flop, do I want to check a hand like this sometimes?
3) If I choose only 1 sizing for my betting range OTF, should that sizing perhaps be 33% instead of my 50?

UTG: 210.53 BB (VPIP: 27.45, PFR: 16.11, 3Bet Preflop: 5.69, Hands: 741)
CO: 251.29 BB (VPIP: 45.00, PFR: 32.22, 3Bet Preflop: 25.97, Hands: 188)
Hero (BTN): 200.39 BB
SB: 199 BB (VPIP: 26.56, PFR: 22.98, 3Bet Preflop: 9.63, Hands: 1,436)
BB: 534.01 BB (VPIP: 31.88, PFR: 23.20, 3Bet Preflop: 2.86, Hands: 330)

SB posts SB 0.5 BB, BB posts BB 1 BB

Pre Flop: (pot: 1.5 BB) Hero has Kc Ac
fold, CO raises to 3.5 BB, Hero raises to 11 BB, fold, fold, CO calls 7.5 BB

Flop : (23.5 BB, 2 players) Qd Kd Js
CO checks, Hero bets 11.75 BB, CO calls 11.75 BB

Turn : (47 BB, 2 players) Kh
CO checks, Hero bets 23.5 BB, fold