[10NL] KK-Value bet river OK?

[GunslingerZ]

This was my first orbit at the table (I won a small pot when I first sat down) so I had no reads on the villain.

I think folding to his river check-raise all in is a pretty simple decision. My main question is, should I have bet the river in the first place? I'm trying to find places to get more value on rivers, and the villain showed a lot of weakness by checking three streets. Should I have checked behind?

Stacks:
* CO with $10.00
* BTN with $5.85
* SB with $15.45
* BB with $6.55
* UTG with $9.95
* UTG+1 with $11.45
* HERO is MP1 with $12.30
* MP2 with $11.55
* MP3 with $10.00

Blinds: $0.05/$0.10
Site: pokerstars
* * Dealt to MP1:K♥ K♣
* * Sklansky group 1
Preflop:
* * 1 players fold.
* * UTG+1 raises $0.20 to $0.30
* * Hero raises $0.90 to $1.20
* * 6 players fold.
* * UTG+1 calls [$0.90]
* * Total folds this street: 7
* * Potsize: $2.55
Flop: 3♦ 10♥ 10♠
* * UTG+1: checks
* * Hero bets [$1.50]
* * UTG+1 calls [$1.50]
* * Potsize: $5.55
Turn: A♦
* * UTG+1: checks
* * Hero: checks
* * Potsize: $5.55
River: 7♦
* * UTG+1: checks
* *Hero bets [$2.50]
* * UTG+1 raises $6.25 to $8.75 [ all-in ]


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[ChuckTs]

Well I like betting bigger on the flop ($2 or so) but otherwise this looks fine. A ten is unlikely, as is a set/fullhouse. An ace is pretty unlikely too given he check-called the flop and checked the river to you even after you check back the turn, but I guess it's still possible. You're basically seeing mostly QQ and under here and I think a value bet is fine. I also like the bet size, 1/2 pot or so.