5/10nl tough spot KK OOP deep(ish) against laggy opponent

[yoyo]

Hero (SB) - $1720
BB - $450
UTG - $187
Cutoff - $1300
Villian (Button) - $2800

Preflop: UTG limps. Cutoff limps. Villian raises to $55. Hero (KdKh) raises to $195. BB folds. UTG folds. Cutoff folds. Villian thinks for long time and calls.

Flop: Jd-Td-4c ($420)

Hero bets $315*. Villian thinks for long time and calls.

Turn: Jc. ($1050)

Hero checks**. Villian thinks for 5 seconds and bets $1210, putting me exactly all-in if I call. Hero folds.

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*Is check-calling an option on this very scary flop? Is check-folding an option on this flop? After the preflop call, I am worried about AA, JJ, TT. I'm marginally behind AKdd (which almost certainly raises flop I think), and I beat QQ. The problem for me is this particular opponent's preflop range is larger (I'd seen him call large pot 3-bets with medium pairs and even suited connectors and suited 1-gappers before against deep opponents).

**The turn check is a planned check/fold for me. Is it standard to give up like this in this spot? I think my opponent is definitely capable of floating in this spot. I suspect it's simply too risky for me, even if he's capable of floating - am I right about this? Does the fact he put me all-in instead of betting smaller change anything?

The more I think about this hand, the more I like the fold, but I suppose I wonder a lot whether I'm becoming very predictable post-flop in situations like this, and how easily good players can exploit this by floating a lot of flops and either letting me over-commit on turn or taking the pot off me if I blink. Is this just a standard fishy concern, or is this just the way the game goes?

(thx in advance)

[beyondcontrol]

Bet the flop like you did, bet the turn, if he puts you all in then you probably have to fold.

He'd most likely raise your flop bet with a set or AA, so I think he has some kind of J or a draw here most of the time. It's also possible that he's calling your flop bet with a pocket pair like 88 or 99 to see if you shut down after the turn. After the J comes on the turn you need to figure out if he has it by betting again. If you check like you did and he's an aggressive player, you're just setting yourself up to get bluffed out of the hand.

[yoyo]

As I had the Kd, I guess that kinda rules out AKdd. Oops.