$200 NLHE 6-max: AK Flops TPTK OoP in 4bet Pot. Best Flop Line?

$200 NL HE 6-max: AK Flops TPTK OoP in 4bet Pot. Best Flop Line?

Villian Stats (VPIP/PFR/AF): 14/9/1.5

Ok, Only 35 hands on villain here, but he seemed to be a reg as he was on both my tables. Not that it means anything but his 3bet was 7.1 and his squeeze was 17 over the small hand sample. I'm assuming he didn't have many hands on me, but I play ~22/20/2.5. Whats his range for flatting the 4bet here? Whats the best line to take on this flop? Bet real small? Check it to him?

poker stars, $1/$2 NL Hold'em Cash Game, 6 Players
Hand History Converter by Stoxpoker

BB: $200 (100 bb)
UTG: $113.40 (56.7 bb)
Hero (MP): $200 (100 bb)
CO: $130 (65 bb)
BTN: $200 (100 bb)
SB: $225.75 (112.9 bb)

Pre-Flop: Hero is MP with A K
UTG folds, Hero raises to $7, CO calls $7, BTN raises to $24, 2 folds, Hero raises to $59, CO folds, BTN calls $35

Flop: ($128) K 3 5 (2 players)
Hero ?

I often bet half pot and get at least floated by TT-QQ, which I expect to be the bulk of his range.

If we check, I think we need to check twice, as checking then betting the turn looks pretty strong.

I prolly vary between shoving & betting like $50.

I probably just overbet shove because I've seen alot of regs snap those off with 2nd pair type hands. They see it as a bluff way more than a psb. I expect villain to see your range heavily weighted towards 1010-QQ and snap off alot here.