KTs vs reg's 3bet

I would fold to 3bet or 4bet pre. We have decent hand against wide range but I prefer not to see flop with this.
As played pre my line would be raise/fold on the flop. Money invested in the pot would be almost same as your line, but we have agression on our side with raising and also I really don't want to see more cards on board.

Villain probably has 15 combos of 88/99/TT that we have fold equity against with a river barrel. He might also have 12 combos of AK and maybe some backdoor spades like A5s/AQs that he played passively which we have fold equity against. Maybe he will fold QJs as well. It doesn't seem like he would slowplay AJ or QQ/KK but maybe he would with AA or JJ. Overall seems like he should have more combos of hands that he will fold to a jam though but its probably also fine to just check and give up here at some frequency. The hand seems well played.

With his wide range villain is quite likely not to have anything on such a dry flop

Which part of this range is going to fold the turn?

So after his small Cbet I decide to float him and try to take the pot later on.

You think villain is thinking the same thing about your turn bet?

I don't know about 4 bet, I need to have more hands and know that he is 3betting lighter from the blinds and button for me to do that. He might end up being very tight after 1000 hands or so. But I guess it would cost the same as the way its played now. But personally, its villain dependent and I am very picky about what range I play against their range.
Below is 11.4% 3bet vs your open and it crushes you. I left all suited A in. Very little folds, he has to have Ax, or KQ, unless he also picked up a spade draw on the turn or a pair, you might fold that on the river, but how much do you have to bet? I'd check the river, sometimes villain is going to show up with something you might have folded with a bet but at least you get the note.

I can't believe I just spent over an hour looking at this hand and playing with ranges before settling on this one, and I missed my tournament

This equiweb has made defining ranges a bit easier for me.

Board: 3♠J♦3♥
Pos Equity Range
CO 21.75% { KTs }
SB 78.25% { 66+,A2s+,KJs+,QJs,AJo+,KQo }
Powered by Equiweb - 6 Max Hold'em Equity Simulations

3B 11% are more les medium pairs + Broasway cards like ATo, KQo, Axs, KTs, pairs 88,99+.
He could have better cards than you like A+Bso, or pairs 99, TT, ....

I'm checking turn.
Non-nut FD (King and a paired board).Very deceptive when we hit. If he checks i fire any river.
Keeps the pot smaller, you don't want to play for stacks on this board with a triple barrel.

Thank for your feedback everyone!

Regarding preflop situation - If you have read on him, fine, you are IP, so I think call PF is quite OK. There are just 5 players and it is 6-max.
After his turn call It looks like he has some pocket pair. There is also posibility of overpair or AJ/KJ, letting you bluff into him.
For me the call of €2,5 is enough for river give up.