I had a very similar spot against the same sort of player which I've posted below. I feel we have to squeeze AQ here but playing OOP when we miss the flop against this type of player makes it really hard to play. I dont like giving up because that seems far too weak given we hold the best hand most of the time on the flop however take this route if you want to decrease variance at the cost of increasing your win-rate. I like the turn jam if he's got say the top 9% of his range and isn't folding the flop then folding then only calling the turn with sets, Jx and Kx he will fold 68% which is enough plus we have 15% equity against that range.
Hero (BB): 132.7 BB
UTG: 115.3 BB (VPIP: 30.87, PFR: 23.50, 3Bet Preflop: 6.90, Hands: 541)
MP: 182.3 BB (VPIP: 58.57, PFR: 27.14, 3Bet Preflop: 20.00, Hands: 70)
CO: 184 BB (VPIP: 14.09, PFR: 8.72, 3Bet Preflop: 2.33, Hands: 306)
BTN: 274.3 BB (VPIP: 29.07, PFR: 18.60, 3Bet Preflop: 6.45, Hands: 88)
SB: 123.8 BB (VPIP: 18.36, PFR: 10.52, 3Bet Preflop: 0.87, Hands: 542)
SB posts SB 0.5 BB,
Hero posts BB 1 BB
Pre Flop: (pot: 1.5 BB) Hero has A
Q
UTG raises to 3 BB,
MP calls 3 BB,
fold,
fold,
fold,
Hero raises to 15 BB,
fold,
MP calls 12 BB
Flop: (33.5 BB, 2 players) J
4
T
Hero bets 15.9 BB,
MP calls 15.9 BB
Turn: (65.3 BB, 2 players) J
Hero checks,
MP bets 31 BB,
Hero calls 31 BB
River: (127.3 BB, 2 players) 7
Hero bets 70.8 BB and is all-in,
MP calls 70.8 BB
Hero shows A
Q
(One Pair, Jacks)
(Pre 64%, Flop 69%, Turn 77%)
MP shows 9
7
(Two Pair, Jacks and Sevens)
(Pre 36%, Flop 31%, Turn 23%)
MP wins 255.5 BB
2.4 BB was deducted from the pot for the jackpot.