I'm pretty sure the button was fishy and the BB had average stats. Can I lay this one down assuming BB has QQ-AA? I felt like I should call the flop c-bet, but with the button's shove I'm pretty much making a commitment decision on the flop. I think a flop fold is right here and I probably would have folded it if I had time to really think out stack sizes and the rest of the hand. Is my call preflop ok?

PokerStars No-Limit Hold'em, $0.25 BB (6 handed) - Poker-Stars Converter Tool from FlopTurnRiver.com

CO ($30.45)
Button ($4.95)
SB ($25)
BB ($26.85)
UTG ($65.10)
Hero (MP) ($47.80)

Preflop: Hero is MP with J, J
1 fold, Hero bets $1, 1 fold, Button calls $1, 1 fold, BB raises to $3.50, Hero calls $2.50, Button raises to $4.95 (All-In), BB calls $1.45, Hero calls $1.45

Flop: ($14.95) 5, 6, 3 (3 players, 1 all-in)
BB bets $8.25, Hero calls $8.25

Turn: ($31.45) 7 (3 players, 1 all-in)
BB bets $13.65 (All-In), Hero calls $13.65

River: ($58.75) 9 (3 players, 2 all-in)

Total pot: $58.75 | Rake: $2.85