KK deep stacked 5 handed at MGM

[snowbank]

I'm in the big blind and pick up KK. 5 or 6 limpers, and I make it $110. 4 callers.

Flop: 347- 2 diamonds

the sb who has about $5,000 bets out $200. He's a pretty decent player, who's been pretty active. I know he's a 2+2 lurker and seems to know what he's doing for the most part. There's still 3 players left to act behind.

If you're hero, what's your plan here, and for the rest of the hand??