We are obviously too shallow to set mine

I am weary of getting it in and then flipping to loose the chip lead, be OOP against the new chip leader and loose my momentum

So do we like simply folding which seems a bit weak to me

What about calling then shoving flops that dont have an ace, king or queen in them which, i would think comprise most of his range when he 3xs?

PokerStars - 800/1600 Ante 150 NL - Holdem - 5 players
Hand converted by PokerTracker 4

UTG: 25,189 (VPIP: 18.42, PFR: 20.00, 3Bet Preflop: 12.50, Hands: 38)
CO: 6,917 (VPIP: 10.57, PFR: 5.22, 3Bet Preflop: 1.09, Hands: 251)
BTN: 17,441 (VPIP: 23.81, PFR: 12.82, 3Bet Preflop: 7.14, Hands: 43)
SB: 20,775 (VPIP: 17.85, PFR: 13.44, 3Bet Preflop: 7.35, Hands: 419)
Hero (BB): 64,678

5 players post ante of 150, SB posts SB 800, Hero posts BB 1,600

Pre Flop: (pot: 3,150) Hero has 6 6

UTG raises to 4,800, fold, fold, fold, Hero ???

I always hate these situations. 5 handed, I would say you are ahead here most of the time so there is no problem getting it in here. Even if you lose, you still have a very healty stack. He probably folds most of his hands here since you cover him. No shame in folding either. I think call and then shove flop is not a good option.

My decicion here is based on whether this REC 3x before and with what hands did he do it. Readless, Im assuming that he's a REC and it's his normal sizing (unless I saw him min raising before). If he didn't min raise before, I shove. If he did minraise and now he 3x, it could mean two things
a) he want to call off vs shorties and does not want you to defend, because he's scared of playing his weakish range postflop
b) he's nutted AF

I flip a coin and click 1 of 2 buttons, as calling and shoving flop is so 2004 and does not make much sense from theoretical point of view.