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Villian is a not so good weakish? Preflop- LAG, i think (actually i dont really know, i'm new to HU ;-) )
After 800 Hands i have following reads:

Steal 66%
4bet: 3%
Fold to 3b: 43%
Fold to cbet: 42%
Fold to turnbet 55%
Raise cbet 3b: 10% (1 out of 10)
WSD: 33%

Well i dont think he has AA-QQ, because he is most likily to 4bet them.
Given our history almost every (but one) Min-X-Raise was weak. Only once he min-X-Raised a straight on 543. Sometimes he continues bluffing, but not very often.

I thin his range is maybe a weak Jx or a T, a set, a OESD, or maybe total Air.
So what is my best play here?

I dont think a Jx, OESD or a set are folding to my raise

1) 4bets KK to $24
2) XminRaises are often weak, gives up to 3b or turn
3) When he stabs smallish in 3b pots he is most likily weak
4) Does not X-Raise turned Trips, X-River again for X-Raise? (Loves to slowplay?)
5) 33% bets not strong
6) smallish stab 33% at turn weak (after X-X Flop)

He plays following style

Poker Stars $0.25/$0.50 No Limit Hold'em - 2 players - View hand 1814274
DeucesCracked Poker Videos Hand History Converter

BTN/SB: $56.23
Hero (BB): $96.54

Pre Flop: ($0.75) Hero is BB with 7 8
BTN/SB raises to $1, Hero raises to $4, BTN/SB calls $3

Flop: ($8.00) 2 J T (2 players)
Hero bets $4, BTN/SB raises to $8, Hero ???

i like betting flop slightly bigger as a std like ~5 with my whole range but it doesn't make a bigger difference, shove (or 3b to 24 or w/e) over the minraise. i don't see a lot of merit to calling.

But if we shove here, we just fold out his complete AIR and we get a great price to call here?

Only because im not sure here.

If we call, there is a chance, that he continues his bluff when a clubs hit and when he wasnt bluffing, we will get his stack anyway, because of his WDS+its a 3bet pot.

its not bad if he folds his air because he's going to have around 40% equity usually. He might bluff clubs but we also don't get the chance to win the pot unimproved as easily.

It's pretty hard to see that board missing him. Any broadway does not want to fold - I would not shove.

I agree this min raise line looks weak - if he has nothing are you confident you can take it away from him on a later street (it sounds like he is pretty weak) - so assuming a yes to that, why not call try to hit your hand, and if you miss you can profitably bluff the river.

given your reads a 3b or a call is fine. It depends on gameflow.
If you got that read that his small raises are weak, I can´t see a reason to fold our hand.

Call preflop.
Its minraise and you have good price and a hand that can call. 3bet 87o instead.

Bet flop bigger, and jam all in when he raises.