KK vs. maniac--I can't respect his raises

[parttimepro]

Playing 1/2 NL at Paradise. Across the table from me is a very loose, over aggressive player who's already lost 3 buyins. He semi-bluffs a lot, and often bets into perceived weakness. He rarely lays down those semi-bluffs to raises or reraises. I've seen him twice go all-in on the turn (and lose) with top pair weak kicker and an inside straight draw. He has $160, I have $300. Three seats to his right is a TAG player who I respect, and who seems to be targeting the LAG (lots of isolation raises).

I get dealt KK on the button. TAG player calls UTG+1, LAG calls, third player I don't have a read on calls. I raise to $10. Blinds fold and all three call.

$40 in the pot, and the flop is 2 6 7 rainbow. All check to me. Your move?

Typically I've been making continuation bets with any board when it's heads-up, but not auto-betting with missed overcards in a multi-way pot. I can either bet my hand ($30-$40) which is almost certainly ahead, or represent AK and check on this safe board, trying to get LAG to attack.