Live €175 tournament in Rozvadov.
6 starting days, 40 minute levels
We started with 50k and are now in the 7th level.

I have 35k left, blinds are 500/1000 with bb ante.
Someone in EP limps.
I have AK and make it 4k
BB calls and the limper calls, everyone else folds.

Pot is 12k
Flop: KJ8r
BB donks for 11k ...
Limper folds.

BB was a VERY bad player.
Constantly telegraphing his hand strength.
Saw him 3bet 5x my open IP with AA.
Saw him shove 70k into a 20k pot with a bottom straight.
Probably some other stuff ...

What our move?

We have 31 bigs left. We don't really have much of a clue of what he's got. We know we got top pair top kicker on a board that isn't really threatening. Calling is out of the question. Really it's only a shove or fold. Online I'm probably getting it in with no read.

Just based on those two things you mentioned (Saw him 3bet 5x my open IP with AA.
Saw him shove 70k into a 20k pot with a bottom straight.) I could find a fold here. Find a spot where we are the aggressor. If a similar spot does come up again we are getting it in.

Another thing you can ask is if he has two pair or trips. If he starts talking you can find a fold. Not all players talk when there strong though so thats gotta be read based as well. If they shrug their shoulders and say nothing when you ask if they have trips or two pair that usually means they are lying meaning they have a good hand so you can find a fold as well.

with the physical tells, and the two patterns you described this hand is a easy fold. without any of it, its easy shove. We would show our hand for meta-game if we fold and look for another player to try this move on us donk-in into us on a similar sort of board or even a draw board perhaps in the near future. The show is read based as well. No point doing it against players who ain't even going to try and exploit you. Players who remember hands and talk a bit of strategy at the table are your mark in this spot.

Would like to hear some more thoughts on this.

What I really struggle with is very simple.
Theoretically I'm never folding here. Don't even care if we're calling or shoving, just never folding.

But in this spot, for whatever reason, I tried to explain in the OP, made me so damn sure this villain is only donk betting pot size with a hand that beats me.
That's two pair or a set. KJ, KK, JJ, 88
Not a lot of hands.

So my feeling was screaming, fold, but my game knowledge was screaming, we can't fold here ...

What was BB´s stack size prior to the 11k-bet?