AJ flop shove

partypoker - $0.10 NL (6 max) - Holdem - 6 players
Hand converted by PokerTracker 4

SB: 85.7 BB (VPIP: 56.90, PFR: 6.90, 3Bet Preflop: 0.00, Hands: 58)
BB: 50.1 BB (VPIP: 21.54, PFR: 21.54, 3Bet Preflop: 13.04, Hands: 66)
UTG: 145.5 BB (VPIP: 59.62, PFR: 25.00, 3Bet Preflop: 5.56, Hands: 52)
MP: 163 BB (VPIP: 33.91, PFR: 8.62, 3Bet Preflop: 2.82, Hands: 177)
Hero (CO): 100 BB
BTN: 247.9 BB (VPIP: 35.31, PFR: 18.13, 3Bet Preflop: 4.67, Hands: 333)

SB posts SB 0.5 BB, BB posts BB 1 BB

Pre Flop: (pot: 1.5 BB) Hero has A♦ J♥

fold, fold, Hero raises to 3 BB, fold, SB calls 2.5 BB, BB calls 2 BB

Flop: (9 BB, 3 players) 6♣ T♥ J♦
SB checks, BB bets 5 BB, Hero calls 5 BB, SB calls 5 BB

Turn: (24 BB, 3 players) 8♣
SB checks, BB checks, Hero bets 15.2 BB, SB calls 15.2 BB, BB raises to 42.1 BB and is all-in, fold, SB calls 26.9 BB

River: (123.4 BB, 2 players) A♣

SB shows Q♣ K♣ (Flush, Ace High) (Pre 67%, Flop 48%, Turn 36%)
BB mucks J♣ 9♣ (Flush, Ace High) (Pre 33%, Flop 52%, Turn 64%)
SB wins 117.3 BB

BB - mid stack reg I guess 20/18
SB - fish 58/8

Normaly I would 3bet on the flop in a 3 way pot like this to prevent the SB from calling, but I hesitated since the reg is a mid stack and I would have to 3bet/call shove which I didn't want at that point. Would that be the best option?
What would you do if I 3 bet, the SB calls and the BB shoves?