Local currency deep stack game in casino (roughly 3$/3$)

Blinds are 25-25, average stack seems to be about 7k there is 3 people with very deep ~10k stack: Hero, Villain and SB

Villain:
Middle aged European, fairly tight and we have only played together in this one game. He bought in with 4k and has built a stack of ~10k.

I have not seen him make any calls with worse hand and I've only seen two hands which went to showdown:

Hand 1: Villain raises from UTG, bad player on tilt 3Bets him from Button, villain 4Bets and bad player calls. Flop comes T-high rainbow, Villain shoves with AK and gets call from QQ but he spikes a K on river and scoops it.

Hand 2: Villain 3bets early position opener who calls, Flop comes paired and with 2 suited cards, he cbets and gets a call, Turn completes flush draw and goes check/check, River the EP leads in and gets a unhappy call from villain with AA which was good and he scoops it.

Hero:
Bought in with 5k, doubled up with nut flush vs smaller flush and had couple of other hands which did not go to showdown that made my stack to be roughly 13k.

Hand:
Straddled hand which I open with KK to 200
Villain 3Bets from Button to 700 and everyone else folds
Hero calls
After thinking briefly I think his 3Bet in button has to be wide so I just flat not to make him fold, hope for no Ace on flop and expect 100% CBet

Pot: 1500
Flop: J63

Hero checks
Villain bets 1200
Hero raises to 3200
Villain thinks a while and shoves all in

After the count Villain had 9800 to start with
Pot is now 13800 and I have to put additional 5900 to it...
Oh boy, here we are with almost 1000BB pot and a meager overpair in hand.

As played would this be a call?
What would be a better line?
4Bet flop would have certainly made this hand easier. Also raise in flop put me to tough spot.
Any pointers about bet sizes?

We're crushed by 15 combos of AA & sets. V has no 2-pair combos (I assume). So, it's a question of how often he's taking this line with QQ, Jx, and draws. If we give him all 6 QQ combos, the occasional Jx, and AKc/AQc, it's a slightly +EV call.

Typically against V's with a wide 3b range, I'd prefer to 4b small for value and set up a more favorable SPR when we're deep.

So I was writing a post to this and had to delete it after really thinking about what you've posted about this villain. I read him as the kind who never believes his opponent can have a hand and because of that, as played I'm going to call. I do not believe he is 3betting 33, 66, j6, j3 or 36. There is so little that he can have that beats you and so much that he can be overplaying. Not to mention that against this particular guy who is prone to overplaying hands it would be criminal to take this line and then fold. You should have a plan for what to do after the c/r if he re raises.

Hand played fine up til now.

Call.

Thanks,

I tanked really long time was afraid of AA and JJ. Was hoping for QQ or AKc/AQc or some smaller pair like TT... but when I called and he flipped over JJ felt sick to my stomach.

I think when he shoves, it reduces the chances of him having a set. He seems like the type who would "call to trap" rather than give you a reason to fold a top pair type hand. I would not in the least bit be surprised to see him do this with a hand as weak as 99 type hands, and would definitely do it with ANY flush draw.

All in all I think he's shoving Jx+ more so than a set

just call his flop bet & soul read any more bets