It would really help if we had some kind of read here. 3betting, calling and folding can all be acceptable. If I 3bet this I would make it $48 with the cold caller.
Standard 3betting for me is 3-3.5x the raise when I have position, 3.5-4x when I am out of position and when there are cold callers I treat them pretty much as limpers. E.g add an extra 1x the open raise per caller. Works for me.
If I checks to us I would probably fire this flop since alot of his range - QQ/JJ/99/88 should fold. However, there is a big argument here for me in favour of a check behind. I like checking gutshots behind because they can't stand a check-raise and we have nut outs so we should take the free card and if he was slowplaying KK/TT we then stack him on turn.
No definitive answer but some points which would influence my decision
Edit: I misread that we were on button. OOP its just a check-fold in a 3 way pot.