$4 NLHE Full Ring: KK vs. min raise on flop, 2/3 pot bet on turn

Villian Stats (VPIP/PFR/AF): 28/14/2.1

Looking for some feedback on turn action for the hand below.

Villain was 28/14/2.1 over 169 hands. Has shown to call 2b from blinds with suited connectors and to play draws aggressively on the turn.

For what felt like a majority of the night, I was getting min-raised on flops where I had an overpair, and ended up staring down a set. What's the turn play here?

Merge - $0.04 NL - Holdem - 7 players
Hand converted by PokerTracker 4

UTG+1: $1.31 (VPIP: 32.53, PFR: 24.10, 3Bet Preflop: 3.45, Hands: 86)
MP: $3.19 (VPIP: 11.98, PFR: 5.15, 3Bet Preflop: 0.94, Hands: 1,572)
CO: $1.07 (VPIP: 16.18, PFR: 9.04, 3Bet Preflop: 3.83, Hands: 805)
Hero (BTN): $6.69
SB: $4.00 (VPIP: 13.62, PFR: 9.08, 3Bet Preflop: 2.42, Hands: 721)
BB: $4.65 (VPIP: 28.05, PFR: 14.02, 3Bet Preflop: 0.00, Hands: 169)
UTG: $6.73 (VPIP: 19.87, PFR: 10.41, 3Bet Preflop: 3.92, Hands: 328)

SB posts SB $0.02, BB posts BB $0.04

Pre Flop: (pot: $0.06) Hero has K♦ K♠

fold, UTG+1 calls $0.04, fold, fold, Hero raises to $0.12, fold, BB calls $0.08, UTG+1 calls $0.08

Flop: ($0.38, 3 players) 4♠ 5♣ 3♠
BB checks, UTG+1 checks, Hero bets $0.25, BB raises to $0.50, fold, Hero calls $0.25

Turn: ($1.38, 2 players) Q♥
BB bets $1.03, Hero ???

Raise more pre. What's villains aggression factor?

I'm only just getting into cash games but I would be tempted to make it 0.18 pre and then fold to the check-raise...

As played I would be folding the turn...

A more experienced player may tell me I'm way off here though...

Reasons for the statements above are mainly the stakes that this is played at, the slightly fishy stats of the villain and that with only a 1BB raise you've probably allowed him to "see a cheap flop" to see if he can catch a flush...

Fold turn, well played.

I've just re-read this and realized you have the Ks..., not folding to the check-raise, still folding the turn...

Thanks for the feedback all. After seeing this situation a few times in last night's session I came to the realization that this has been a typically spewy spot in my game. Will be working to clean it up this month and hopefully save some bb.