Checking the lines, KK on BB

[CanYouCallThis]

First hand I'm putting here, kinda guess the awnser but wanna check the lines on Hero. No stats on villain.

PokerStars No-Limit Hold'em, $0.25 BB (8 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

UTG ($5.60)
UTG+1 ($20.85)
MP1 ($25.30)
MP2 ($17.50)
CO ($14.40)
Button ($38.05)
SB ($24.15)
Hero ($25)

Preflop: Hero is BB with K, K.
[color=#666666]2 folds</font>, MP1 calls $0.25, [color=#666666]4 folds</font>, [color=#CC3333]Hero raises to $1</font>, MP1 calls $0.75.

Flop: ($2.10) 8, 7, 4 [color=#0000FF](2 players)</font>
[color=#CC3333]Hero bets $1.5</font>, MP1 calls $1.50.

Turn: ($5.10) 2 [color=#0000FF](2 players)</font>
[color=#CC3333]Hero bets $2.5</font>, MP1 calls $2.50.

River: ($10.10) 5 [color=#0000FF](2 players)</font>
[color=#CC3333]Hero bets $4</font>, MP1 calls $4.

Final Pot: $18.10

I thought about checking the turn when I saw the hand, but then figured the turnbet was going to get called by loads of worse/drawing hands, and I figured it was likely Hero was still ahead.

Would it be smarter to C/C the turn? Or a smaller valuebet on the river?