As you know Im a beginner so take my advice here with a big grain of salt, as im especially uncertain about 3betting. I am just learning about smoothness and I actually think that despite the double suite your hand isnt that smooth, meaning there will be quite some flops where you flop poor EQ. So even though you do have the stronger hand preflop and will get called a lot by worse hands, the fact that youre also OOP and he is aggressive would incline me to just call.
On the flop I do not like the check/call. Unless you hit a K on the turn you will end up folding a lot. Even if you hit backdoor draw, he might still bet big and I dont think you can call.
I think I would just go ahead and bet 2$. He can still call with worse and if he folds some EQ its always good. If you turn a backdoor flushdraw I think its much better to be in the position of firing a 2nd barrel than having check/called the flop and now having to check/call again.

Agree with Gamblling Poet about postflop line.

Regarding the 3bet, I wouldn't do it. Not because the hand has polarized Eq distribuition (that's the kind of hand I prefer OOP), but because stacks are so deep that it won't do much for you. Against described villain, we can argue about 3betting in a regular 100bb deep situation to try to push a Eq edge, an deny him positional advantage.

But here, you are just inflating the pot in a situation where you are most likely to fold in future streets (being OOP, with a polarized hand and a a SPR of 10)

Ps.: Being a 54/28/14 who OR BTN 68% isn't a guarentee that he is fish IMO, specially considering samplezises issues and the fact that the table is deep, where you can get away playing a wider hange IP.

3bet is good. Since you checked and he pots you should probably fold as he will probably continue with the same bet size on any turn and wont give you odds to call on say a backdoor flushdraw card. You might also not even have implied odds on a king even if you think you do since he could very easily just try to bluff with a naked jack and the most you will win on a king will be another pot bet and it's not worth it given how rarely you will hit it. I think cbetting is bad, you will almost never get a fold on this board and you will get floated slowplayed and bluffed a lot. I'd put this hand in my c/c range against normal bets but fold against a pot.

You crush his range mainly. You get to have more top set on Kxx, high flushes/flushdraws. This should be 100% 3bet in this situation, why wouldn't you 3bet? Yeah you're deep and it's tougher to play but still the pros far outweigh the cons.

In case Opponent is Loose-Aggressive or a Fish, you get his stack anyway. Wait for the right spot. I like your play.

When you check-call the flop, what turns are you looking for? What turns you check-fold, check-call or check-raise? Are there any turns you would donk?

IMO you should either bet yourself or check-fold. Half of the time you will get a flushdraw on the turn, but even then it sucks to play oop after a check. You just have to check-fold on so many turns, that it's better to save your money if you don't like to cbet the flop.

Thanks guys. Good to see so many feedback. Regarding the hand: the guy got a note that he is pot potting this flop after i check where i have 3bet pre. Next time im check calling with top2+ and check shove the turn.

BTW what do you think about cbettinng pot vs cbetting 2/3 OTF. For: just take it down there and discourage light peels. And if he happens to call my potcbet he may not feel potting the turn after my check. Or is it better to just give up and exploit his tendencies later?..