$200nl - Overpair flop commitment decision w/KK

Button is unknown and I'm pretty sure this was his first or second orbit at the table. Other two villains are about 18/9/0.9 over a lot of hands.

PokerStars No-Limit Hold'em, $2 BB (9 handed) Poker-Stars Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

CO ($276.35)
Button ($106.45)
SB ($98.40)
BB ($261.60)
Hero ($196)
UTG+1 ($211)
MP1 ($203.65)
MP2 ($197)
MP3 ($228.90)

Preflop: Hero is UTG with K, K.
Hero raises to $8, 4 folds, CO calls $8, Button calls $8, 1 fold, BB calls $6.

Flop: ($33) 8, J, 7 (4 players)
BB checks, Hero bets $28

I make this bet with the plan to fold to a raise from CO or BB and call a push from the button.

Thoughts?

You're representing a strong Jack or better, maybe the nut flush draw. I'd say anyone who raises has AJ or a better made hand. Also, the BU shove would give you about 3:1? The plan sounds good. No time to act weak now.

Hero rarely has Jx here.

It's AA-QQ/set far more often.