AA vs fish - good overbet spot or turning a hand into a bluff?

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AA vs fish - good overbet spot or turning a hand into a bluff?

Blinds: $0.10/$0.25 (6 Players) BN: $41.06 (Hero)
SB: $36.23
BB: $34.61
UTG: $12.84
MP: $42.63
CO: $21.49
Preflop ($0.35) Hero is BN with A A
3 folds, Hero raises to $0.73, SB folds, BB calls $0.48
i open bigger, cause the BB was a fish.
Flop ($1.56) K 7 9
BB checks, Hero bets $1.16, BB calls $1.16
He wasn't particularly aggro on any street, so I just plan to B-B-B this one.
Turn ($3.88) K 7 9 6
BB checks, Hero bets $3.20, BB calls $3.20
River ($10.28) K 7 9 6 9
BB checks, Hero bets $12.60, BB calls $12.60
I thought that he doesn't really have 9x [besides 89s, T9s (4)], but he's going to have Kx so much more often. Also, the FD missed, as well as some KQ/QJ/JT stuff, so I wanted to polarize my range as much as I could to get max value. I think I could have gone a little bigger, like 15-16$.

Thoughts?

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