Help me not suck in 4bet pots

We'll just get the solver solution out of the way. Solver is pure jamming this over the raise (lol wtf) and snap calling turn.

Hand History driven straight to this forum with DriveHUD 2 Poker Tracking Software

NL Holdem 2(BB)
HERO ($203.50) [VPIP: 28.9% | PFR: 24.1% | AGG: 36.7% | Flop Agg: 41.7% | Turn Agg: 33.8% | 3Bet: 11.5% | 4Bet: 14.2% | Fold to 4Bet: 56.9% | Hands: 313415]
BB ($200) [VPIP: 48% | PFR: 40% | AGG: 41.2% | Flop Agg: 33.3% | Turn Agg: 50% | 3Bet: 8.3% | Fold to 3Bet: 50% | 4Bet: 0% | Hands: 26]
HJ ($340.06) [VPIP: 26.9% | PFR: 15.4% | AGG: 0% | Hands: 26]
CO ($265) [VPIP: 24% | PFR: 16% | AGG: 37.5% | Hands: 26]
BTN ($215.65) [VPIP: 40% | PFR: 0% | AGG: 66.7% | Hands: 5]

Dealt to Hero: A♥ K♥

HJ Folds, CO Folds, BTN Folds, HERO Raises To $6, BB Raises To $16, HERO Raises To $40, BB Calls $24

Hero SPR on Flop: [2 effective]
Flop ($80): 7♦ 2♣ 7♥
HERO Bets $19.25 (Rem. Stack: $144.25), BB Raises To $64.50 (Rem. Stack: $95.50), HERO Calls $45.25 (Rem. Stack: $99)

Turn ($209): 7♦ 2♣ 7♥ 7♣
HERO Checks, BB Bets $95.50 (allin), HERO ?