KK 135 bb deep

[muse1983]

Brief history: A little while ago I had an absolute maniac to my left who raised like 3/4 of the hands he played and called reraises with most of them. He was the main reason I was at the table.

In one hand he minraised, I 3bet with JJ and villain 4bet, I folded. A little while later the exact same situation came up, only this time when villain 4 bet I pushed because I figured that he thought I was isolating the maniac and that he was restealing from me. He called with KK. Needless to say, 2 hands are not an adequate sample size to justify pushing JJ pf. He seems like a tight, decent player and except for that hand we haven´t tangled at all.

For this hand I´m interested whether my flop bet size is ok and whether I should

a) push the turn
b) check behind
c) bet smaller

On to the hand:

Seat 1 is the button
Total number of players : 5
Seat 1: hero (button)( $135.60 USD )
Seat 2: sb ( $82.08 USD )
Seat 3: bb ( $99.88 USD )
Seat 4: villain (utg)( $220.28 USD )
Seat 6: mp ( $93.77 USD )

** Dealing down cards **
Dealt to hero [ Ks Kd ]
villain raises [$4 USD]
mp calls [$4 USD]
hero raises (16 USD)
sb folds.
bb folds.
villain calls [$12 USD]
mp calls [$12 USD]
** Dealing Flop ** [ 4c, Qd, 3c ] Pot = 48,50$
mp checks.
hero bets [$34 USD]
villain calls [$34 USD]
mp folds.
** Dealing Turn ** [ 5d ] Pot = 116,50$
villain checks
hero is all-In for 85$