$100 NL Jacks OOP on K-K-8 board.

[Malachii]

Playing 8 handed, 1 limp, folded to me in the SB with JJ (suits not important.) I make it $6. BB folds, limper calls. Effective stacks $100. The limper lost a stack where he got all in with a flush draw + gutshot versus a higher flush draw about ten minutes ago. He seems pretty solid.

(12$ in the pot)
Flop comes K-K-8 rainbow. I bet 8, he calls.

($28 in the pot)
Turn comes another K.

What the best way to maximize value here? Check/call, checkraise, or bet? I think I stop betting on the turn too often in these situations and what to hear what 2+2 has to say.