Early in WSOP Event #25 - Best line with a set?

[DP388]

Early on I felt I got bet out of a few pots and it looked like I may have been playing passive. The villian in this hand maybe saw a couple of those, but he was late to the table so I'm not sure how many he saw. Villian is a younger guy and an internet player. He seems confident and has been aggressive.

Because of those hands, my stack was down to about 2,800 from the 4K starting stack. Villian has about the same amount. Here's the hand.

Blinds at 25/50 and I make it 150 from middle position with 88. Villian calls in the cut-off and everyone else folds.

Flop is K86 rainbow. 375 in the pot.

I decide to lead out for 200 and villain thinks for a second and calls. I think there is a good chance he has a K (like KQ, KJ), possibly a mid PP or also 97. He could also just be playing position.

Turn is a 2. Pot is 775.

I love checking here against an aggressive player who thinks I was just c-betting, so I check. He bets 625.

Pot is 1400 and I have about 2450 left.

What is my best line moving forward?