Hero: I've been at the table for 20 minutes or less. I limped once in LP with a pp, missed and folded. I called on raise IP against V in this hand, folded to his cBet when I missed and player to my left looked like he wanted to call (and did). Bought in for $200, and I'm sitting on around $220 at the moment.

Villain: BTN. Raised at least once in LP (and I think once from the BB but I'm not positive.) Both times it was $12. He's ~40, looks like he's played poker some, likely family man, just here relaxing before he goes home. Covers hero.

HJ: Looks pretty unhappy about the whole situation. He's got $130 total. I expect him to play his hand very face up. Fold 66-/AQ-, call 77-JJ, AK, ship QQ+.

Pre:
All fold to HJ
HJ raises to $10.
BTN raises to $20
Hero in the SB with JJ.

What to do?

I'm pretty unsure what to do here and later based on what actually happens in the hand.

Flat the 20 if HJ wants to raise he is shoving. So you can polarize his range and fold. If her flats you are set mining and barreling if you are the over pair folding to aggression. I am not shoving bad idea.

I would just flat this unless you thought a really big raise could take the pot down. But your hand plays well here even though you're OOP and you gain a lot of value with a favorable flop.

If you flat, you are set mining. Just so you're aware of that. You can maybe c/c a c-bet on a low board, but that's it.

If you 4-bet, you are 4-bet/folding. He's NEVER 5 betting here with worse, and rarely with a flip.

Personally, I would 4-bet/fold here to $40. If called, I would c-bet any flop that doesn't have an A or K on it, and be done with the hand unimproved if called/raised.

How nitty is folding, guys? I might have a problem.

If called? Who is ever putting in a 3-bet there and then folding to a tiny 4-bet when they have position? Either you are going to get called and have to play this semi-awkwardly bloated pot against a V who could have a wide variety of hands or you are getting 4-bet and having to fold.

I guess if this is your "How can I find out he has me beat and only lost $40" plan, it might work that way some of the time. But more often that not your small 3-bet is going to cost you more than that.

I considered folding, raising and flatting.

Which is why I'm here questioning the crowds.

With 110BB OOP and two raisers behind you with one being short stacked I definitely see the argument for flatting the tiny 3 bet and set mining if HJ just calls 20 also, and folding to a 4 bet.However in a spot like this I think the question is what play helps us define Villains range cheapest but still gives us opportunity to win big. Again it seems like flatting is right as we only lose 20 to a shove and we double through more often than not with a set here. In this spot, for me at least I like 4 betting to 55. Sure, flattening a button's 3bet puts us ahead of a good portion of his range and HJ's range. OOP with your stack size I want to have as much info as i can possibly have so I'm not guessing on 853r flop. I landed on 55 because i feel HJ has a hard time calling over 35% of his stack and he folds hands like KQ and AQ which play well against JJ. If he shoves it's a snap fold and he still may call 88-1010 here but never QQ-AA+AKs. Now the button will be influenced by what the HJ does but nothing we shouldn't be able to handle. Three handed with this much dead money he never flats KK-AA. With 130 in pot and only 35 to call BTN will call call with a wide range of hands we beat and will probably only flat QQ which beats us and AK which we flip with. If HJ folds it does open up possibility of button flatting with KK and AA in postion but I feel 88-1010 are calling more often as are A10s-AKs needing just 35 to call make 120 chip pot. Only hand I feel susceptible to is QQ as Villain could play this hand many ways