Villain is 14/10 with 3b% of 3 over 635 hands. He is very much capable of restealing.

PF: I called 3bet as I suspected villain of restealing, and that he would fold worse hands to any 4bet. Is the reasoning fine?
Flop: Here is where I think I made a mistake. Should we be reraising flop to protect whatever equitywe have with the intention of folding to a 3bet?
Turn: As played, can I call this double barrel?
River: EZ fold?

Poker Stars $0.25/$0.50 No Limit Hold'em - 7 players
The Official 2+2 Hand Converter Powered By DeucesCracked.com

SB: $61.85
BB: $52.00
UTG: $50.75
UTG+1: $55.10
MP: $50.75
CO: $14.50
Hero (BTN): $71.80

Pre Flop: ($0.75) Hero is BTN with J J
4 folds, Hero raises to $1.50, 1 fold, BB raises to $5, Hero calls $3.50

Flop: ($10.25) 3 T 9 (2 players)
BB bets $5.55, Hero calls $5.55

Turn: ($21.35) K (2 players)
BB bets $11.15, Hero calls $11.15

River: ($43.65) 9 (2 players)
BB bets $30.30 all in, Hero folds

I might be a little weak but I fold JJ to 3bets unless villain 3bets 10%+.
Even if no king came you are not likely to beat anything people 3bet with. Expect QQ/KK/AA to own you if you ship that flop, and the way he continued betting on all streets I think he has Aces, less likely kings. But I play nl10 so i might be wrong xD

EDIT: if you think he was restealing, calling is fine. Once he bets all his stack in 3 streets we only beat a bluff, he can even 3bet KJ/KQ as a resteal and go nuts once the king comes.

A call pre seems fine. We don't want to get shoved on and if you think he resteals then playing in position with JJ is all good to me.

I don't see any point in raising the flop for exactly the same reason we didn't 4bet pre. It stops him continuing with worse.

This might be a little retrospective of me, but even though his turn bet offers us a good price, it looks a lot like he's setting himself up to shove the river nicely. And the K isn't a good card for us.

I think we can find a fold on the turn, but I always feel like a nit. Saying that, overcalling is my biggest leak.

It's hard to put him on a 3barrel without a better hand. If you fold here, I wouldn't complain about the rest of the hand really (though I think folding turn might be optimal).

fold the turn ainec

I think this hand is more complicated then it seems.

PF we raise for value, which looks like a steal, Vil resteals and I assume fron these stats he is a reg, so he has a polarized range here.

Vil range is AK+ KK+ A2-A5s 22-55 ish + or - some Kxlow some SC's.

We have position so our hand is definitely playable, however the value of our hand is low. We do not have odds to setmine here. We have showdown value here, but calling 3 streets in a 3bet bot with JJ is not going to be profitable so we should have a plan for this hand knowing we will not be able to take villain off his hand if we run into the top of his range.

I think a clue in this pot is his bet sizing PF. Villains bet sizing does not make sense in that when your range is weighted towards junk, why would you make your standard 3bet larger - to $5. A constant $4.50 3x would be more profitable, so without any other knowledge on this vil's bet sizing I would say he is more likely to have something on the top side of his range.

I think between
Fold
Call
3bet

I wouldn't say any of the above is wrong here, it depends how you want to play the hand against his range, as long as you have an idea BEFORE you make the decision of what to do PF you should be ok.