Don't know what to expect from his limp-3b range, it's probably just about the same a limp-call, I guess.

PokerStars - $0.02 NL FAST (6 max) - Holdem - 6 players
Hand converted by PokerTracker 4

Hero (BTN): 100 BB
SB: 264.5 BB (VPIP: 40.00, PFR: 40.00, 3Bet Preflop: 50.00, Hands: 5)
BB: 111 BB (VPIP: 0.00, PFR: 0.00, 3Bet Preflop: 0.00, Hands: 4)
UTG: 142 BB (VPIP: 17.24, PFR: 12.07, 3Bet Preflop: 0.00, Hands: 59)
MP: 168.5 BB (VPIP: 11.11, PFR: 11.11, 3Bet Preflop: 50.00, Hands: 10)
CO: 175.5 BB (VPIP: 22.08, PFR: 18.18, 3Bet Preflop: 8.00, Hands: 80)

SB posts SB 0.5 BB, BB posts BB 1 BB

Pre Flop: (pot: 1.5 BB) Hero has J J

fold, MP calls 1 BB, fold, Hero raises to 4 BB, fold, fold, MP raises to 15 BB, Hero calls 11 BB

Flop: (31.5 BB, 2 players) 2 T 8
MP bets 16 BB, Hero calls 16 BB

Turn: (63.5 BB, 2 players) 2
MP checks, Hero checks

River: (63.5 BB, 2 players) A
MP bets 35 BB, fold,

1/3 pot on the turn to charge his overcards. When he checks I'm done giving him credit for QQ+ unless he check raises or something.

I'm honestly probably 4-betting this vs a limp-3 bet. As played, firing turn seems reasonable, he can certainly call with worse, and he's already shown that he does not know how to play preflop, so post-flop is probably going to be even worse. I think this is a monsters in the closet hand, we have an overpair, and villain checks when the board becomes more coordinated. Whatever he has, he is not playing his hand correctly. I like firing like 38bb on turn, curious to see what other people might reccomend. AP, I don't know if we can call river. A is a terrible card, but we have under-repped our hand somewhat. Looks like a value sizing, but the price is so nice, 3:1, he only has to be bluffing 25%, and he has no idea what he's doing. If we fire turn, we might get to check this river down possibly, or he might fold out some of his ace highs that barreled the flop and checked turn.

I would try to get the money in pre
bet the turn for value, 1/2p should be good, maybe a bit less

30% bet ott

I think you need to give the limp/raise respect. Basically treat it as you would a 4-bet while deep stacked. Limp/raises indicate monster strength hands. On occasion you'll see bluffs as well. I would definitely call it preflop. Raising yet again is a massive mistake imo. You'll mostly be stacking off against a range of QQ+ and AK.

I either play the hand the same way as you or jam the turn. It is close. I think I like check turn a little better since he can bluff the river or you can get small value from AK.

Definitely fold this river though.

NH. Limp/4-bet should be pretty alarming although I have seen some players (<75bbs) at the micros do this with small PPs, but population reads tell me that with V deep stacked more than likely at best you're flipping pre. River is a fold.