10NL : Yuk 3bet pot spot on flop

Villian Stats : (VP$IP/PFR [Street Aggression] 3-bet%)

CO: 29/12 [3 3 inf] 0% over 35 hands.
BTN: 19/9 [2 1 9] 2% over 199 hands.

My Thoughts And Questions

Ok so here is my problem if i dont 3bet JJ here i am OOP on two players. When i 3bet JJ it leaves a pot bet nehind for the initial raiser when he calls. This is fine cos A/K/Q flop are in the minority so my raise must be +EV.

So how do i now proceed on this flop ? check and hope he bluffs with hands like 88-TT AQ etc ?

Poker Stars $0.05/$0.10 No Limit Hold'em - 5 players

CO: $5.55
BTN: $22.00
SB: $12.50
Hero (BB): $12.30
UTG: $12.20

Pre Flop: ($0.15) Hero is BB with J:heart: J:spade:
1 fold, CO raises to $0.40, BTN calls $0.40, 1 fold, Hero raises to $1.60, CO calls $1.20, 1 fold

Flop: ($3.65) 7:heart: 2:club: K:diamond: (2 players)
Hero?

I'm not folding. So it's either shove or check/call. If you shove you have a shot at folding out QQ, possibly KQ if he convinces himself that I'm doing this w/ AA or AK and not giving a free card to improve AQ/AJ/AT. In addition, he may call behind 'cause he's already got damn near 1/3 of his stack in the middle.

If you check you MAY snap off a bet from AQ/AJ/QQ but my bet is that it's more likely that he'll take advantage of his position and see a free card. Then what are you going to do if a Q or an A hits the turn? Check/fold?

Given stack size, that I'm not folding here and I'm not giving him a free card to improve, I'm shoving.

A/K/Q flops happen like 50% of the time

this is definitely not a yuk spot, if you want to make it easy just openshove or bet pot/call