how to get max value here vs Reg?

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how to get max value here vs Reg?

Blinds: $0.01/$0.02 (9 Players) BN: $1.95
SB: $2.03
BB: $1.88
UTG: $2.19
UTG+1: $0.58
MP: $2.43
MP+1: $2.11
MP+2: $2.25 (Hero)
CO: $2.04
Preflop ($0.03) Hero is MP+2 with K A
UTG raises to $0.06, 3 folds, Hero calls $0.06, CO folds, BN calls $0.06, SB folds, BB calls $0.04
Flop ($0.25) 8 A 8
BB checks, UTG checks, Hero bets $0.15, BN folds, BB calls $0.15, UTG folds
Turn ($0.55) 8 A 8 Q
BB checks, Hero checks
River ($0.55) 8 A 8 Q 2
BB checks, Hero bets $0.27, BB calls $0.27
Final Pot MP+2 wins and shows two pair, Aces and Eights.
MP+2 wins $1.05
Rake is $0.04

Villain 16/8 reg or so...

on the turn it's very obvious that he either has a weak 8x a strong 8x and far more often a weaker Ax than mine.
The problem is though that if I bet turn he is gonna fold a ton of Ax like all the nits do so I thought that I might get more value by checking turn and betting river.

On the River in his view he splits vs everything but AK+ so maybe I can go for 2/3 potsize OTR but imo people tend to fold vs 3/4 pot or higher so the perfect betsize is probably between 1/2 and 3/4... how big would you have bet considering this is FR and we play vs a supernit -.- ?

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