2-5 what would you do?

Played fine to this point. Check/call the turn and evaluate the river. Your opponent's range is wider than you think, he has plenty of stuff that isn't JX. If the turn checks through, value bet river yourself.

Yeah pretty much what Dan said. Check turn and call any reasonable-sized bet.

Preflop and flop sizes are debatable, but it depends how you craft your entire strategy.

He is opening with a wide range on the button, and will likely have a lot of marginal hands. So considering how strong your hand is, I actually like only making it 4x like you did to encourage him to continue with more hands against your kings. In a vacuum with no history, I would prefer to make it 5x with my light 3-bets when I'm encouraging folds. Now obviously if you have history with the player you probably want to size your 3-bets the same regardless of whether you're strong or weak.

Anyway my point is that your sizing was fine and 4x or 5x are both reasonable. Your flop sizing is also within the bounds of what would be considered reasonable, but again it depends what you're doing with your entire range.

Villain profile would be helpful
Is he even capable of a bluff?

I like the previous advice, but if he’s aggressive, capable of claiming that Jack and making things miserable, I’d probably bet the turn to discourage that line. You’re less likely to bluff someone that keeps barreling.

Otherwise, betting the turn will fold all the worse hands and only get called by better, so check’s good.

If villain shoves turn, do you credit him with a jack and fold?
If an ace hits the river and villain shoves do you give him credit and fold?

From villain’s POV
If I can represent a jack or an ace and get kings to fold, I might should be taking more chances in situations like this.

Let me summarize the advice in this thread so far....

"He has lots of hands you can beat, soooooooooo check"

What timeline am I even in??

There aren't a lot of Jx hands that can 3bet out of the blinds so V likely knows you didn't connect with this flop. Thus, he's likely floating the flop with lots of hands. In addition to his jack hands, he's got middle pocket pairs, he's got AQ/AK, he's got T9, maybe T8s. He can have 45s, 56s too.

The whales in this thread think you should let those hands draw to the river for free.

I promise you that's a losing play.

bet/fold.

So you are saying your advice would be to bet and if he raises fold? If so how much do you think you should bet? If he calls the bet would you check/fold on the river?

Yes. Actions are often expressed as the action and the response to a bet or raise. e.g. bet/fold, bet/call, check/call, check/raise. My advice is to bet/fold the turn.

Sizing is always going to be situation dependent. Here, our villain's range is Jx, 88-TT, Ace-high, and a smattering of gutshot straight draws. Much of that range will fold to any bet. I would choose a small size that targets the middle pairs for value and loses the least against Jx. Probably around $80

I'll most likely have the same thinking on the river. I'd bet/fold for 1/3-ish pot targeting his medium strength hands. Though that could change depending on what river card comes.

Yes. Much bigger than less than half pot. Probably closer to 3/4-pot than this size tbh. Flop is the one street where a lot of his range(which should be wide) will click call.
No.
Pre seems fine.

Turn is probably(?) better as a check. I'm guessing in theory we probably mix between check and bet but in practice we'll fold out all the draws and small PP that theory calls making turn bet less good in practice.

Interesting hand.

I would ignore his advice. He's a 2nl playing troll.