I guess it looks super strong to re-reraise like I did on the flop. I think I would have preferred to just all in, but perhaps a call is also ok? Though I think all-in is best, instead of calling and V gets a flush on the turn.

I suppose it's not quite min re-reraise, but it is very small and just looks like you are begging V to go all in.

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

BTN: 75 BB
SB: 49.5 BB (VPIP: 40.00, PFR: 40.00, 3Bet Preflop: 0.00, Hands: 5)
BB: 101.5 BB (VPIP: 29.67, PFR: 25.27, 3Bet Preflop: 7.89, Hands: 92)
UTG: 131.5 BB (VPIP: 25.93, PFR: 25.93, 3Bet Preflop: 0.00, Hands: 27)
Hero (MP): 100 BB
CO: 113 BB (VPIP: 24.58, PFR: 20.34, 3Bet Preflop: 9.62, Hands: 120)

SB posts SB 0.5 BB, BB posts BB 1 BB

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

fold, Hero raises to 3 BB, fold, fold, fold, BB calls 2 BB

Flop: (6.5 BB, 2 players) 6 9 J
BB bets 4.5 BB, Hero raises to 13 BB, BB raises to 29.5 BB, Hero raises to 49 BB

Lol just save time and 4bet shove the fish
You're also giving him a really good price to call with your 4bet.

Either shove flop or call flop -> GII on the turn IMO. I think I prefer the former.

I'm confused about what your sizing accomplishes. It's not like he's making a mistake by calling the draws in his range to our almost-min-4-bet.

If we shove, then he's not folding worse sets, and he's put in a rough spot with most of his draws. When we shove flop, he has to call 67.5BB to win 133BB, so he needs about 34% equity. Probably a little higher after rake is removed. I put a range of Ahxh, KhTh, QhTh, and 7h8h into Equilab, and against our specific hand, Villain only has 29% equity with draws. So when villain has draws, he either calls without the correct equity, or he folds with a decent amount of equity after bloating the pot. Either option seems good.

The other option is that we call flop and try to GII on the turn, since I imagine villain is likely to fire turn on most cards (we also have a lot of draws in our range after the flop). I guess this option is better when villain is likely to fold some portion of his range to a flop shove that would otherwise bet turn? Just not sure how wide that part of his range is.