What should I be getting 3 streets of value with?

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Posted by posted in Low Stakes

What should I be getting 3 streets of value with?

Blinds: $0.01/$0.02 (6 Players) BN: $4.05
SB: $1.42
BB: $2.52 (Hero)
UTG: $1.61
MP: $2.66
CO: $2.49
Preflop ($0.03) Hero is BB with X X
3 folds, BN raises to $0.05, SB folds, Hero raises to $0.19, BN calls $0.14
Flop ($0.39) 5 4 K
Hero bets $0.17, BN calls $0.17
Turn ($0.73) 5 4 K 6
Hero bets $0.34, BN calls $0.34
River ($1.41) 5 4 K 6 Q
Hero bets $1.32, BN calls $1.32

No prior history, he looks me up quite quickly with JJ. Given this information, how would you adjust the 3barrel for value range here? (I never 3barrel bluff here, hence I am sure I should widen my range from solely AK, KK, AA and occasional set vs him.)

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