10NL - Checking back KK after RaiseCB in 3bpot

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10NL - Checking back KK after RaiseCB in 3bpot

Blinds: $0.05/$0.10 (4 Players) BN: $10.00 (Hero)
SB: $10.25
BB: $10.00
CO: $10.10
Preflop ($0.15) Hero is BN with K K
CO raises to $0.30, Hero raises to $0.90, 2 folds, CO calls $0.60
Flop ($1.95) 5 4 Q
CO checks, Hero bets $0.63, CO raises to $1.85, Hero calls $1.22
Turn ($5.65) 5 4 Q 3
CO checks, Hero checks
River ($5.65) 5 4 Q 3 T
CO bets $3.65, Hero calls $3.65

20k hands from 23/18 reg
54% f3b from CO
4% 4brange from CP
41% fold to CB in 3bpot
8% raiseCB in 3bpot

Since I bet 1/3, I believe his XR will be wider than his standard XR range.
Turn blanks up and he checks. Since we're holding the Kd, is okay to check back here ott?
When he bets 36,5bb ott, he has 37bb left only.
Is fair to raise here? 'Cos he is pratically commited here. Or just call as played?

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