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[5z] Isolation the limper

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[5z] Isolation the limper

Blinds: $0.02/$0.05 (6 Players) BN: $7.35 (Hero)
SB: $7.13
BB: $5.51
UTG: $12.66
MP: $5.00
CO: $7.61
Preflop ($0.07) Hero is BN with K 5 A T
2 folds, CO calls $0.05, Hero raises to $0.22, 2 folds, CO calls $0.17
V is very loose and very passive playing 64/5/0 in my ~100 hands with him.
Flop ($0.51) A K 3
CO checks, Hero bets $0.30, CO calls $0.30
Turn ($1.11) A K 3 9
CO checks, Hero bets $1.07, CO calls $1.07
Betting pot here should not be standard, however I figured there would be a good chance that his calling range is entirely unelastic and he will peel whatever he wants to peel anyway. Of course we are ahead of that and can use this to extract maximum value.
River ($3.25) A K 3 9 7
CO bets $1.56
Folding, calling and raising (as a bluff) could all be possible depending on the assumptions we make on his play. Thinking about the hand afterwards I still cannot figure this out. Please help!

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