KK in weird spot

Villain is unknown.

Would he raise boats here on the turn? There shouldn't really be any 4s in his range.

Does the Kh make a ship here ok?

Full Tilt Poker, $0.50/$1 NL Hold'em Cash Game, 5 Players
LeggoPoker.com - Hand History Converter

BB: $84.75
Hero (UTG): $119.60
CO: $112.35
BTN: $264.55
SB: $162.80

Pre-Flop: K:heart: K:diamond: dealt to Hero (UTG)
Hero raises to $3.50, CO folds, BTN calls $3.50, SB calls $3, BB folds

Flop: ($11.50) 4:heart: 2:heart: 7:heart: (3 Players)
SB checks, Hero bets $7.75, BTN calls $7.75, SB folds

Turn: ($27) 4:club: (2 Players)
Hero bets $19, BTN raises to $42, [color=red]Hero?

I bet bigger on the flop, bigger on the turn and shove/call turn raise vs. an unknown.

I think this can be a fold with a better read on a nit/TAG as we don't beat much. But unknown, I'm stacking off.