5NL 6-Max - Getting bet into with full house on river

[kleitches]

Stacks:
* Quie with $8.74
* BTN with $4.45
* SB with $7.83
* BB with $6.00
* UTG with $1.54
* MP with $6.10

Blinds: $0.00/$0.00
Site: pokerstars
Dealt to BTN:7♣ 6♣
* * Sklansky group 5
Preflop:
* * 2 players fold.
* * quie raises $0.10 to $0.15 Hero calls [$0.15]
* * SB calls [$0.13]
* * 1 players folded.
* * Total folds this street: 3
* * Potsize: $0.5
Flop: A♦ 6♥ 6♠
* * SB: checks
* * Quie: checks Hero bets [$0.25]
* * 1 players fold.
* * SB calls [$0.25]
* * 1 players folded.
* * Total folds this street: 1
* * Potsize: $1
Turn: 3♠
* * SB: checks Hero bets [$0.60]
* * 1 players fold.
* * SB calls [$0.60]
* * Potsize: $2.2
River: 3♥
* * SB bets [$0.60] Hero raises $2.85 to $3.45 [ all-in ]

Is shoving on the river here the right move? I don't see calling as getting max value, but I guess the argument could be made that I'm only going to get called by better hands. Given that SB flats PF and shows weakness throughout the hand, was this my most viable option?
https://www.cardschat.com

 

[c9h13no3]

1) Bet more on the flop, I'm thinking $0.40-$0.45. This sets you up so that you can get all in on the river without him donking into you or over-betting.

2) Again, bet more on the turn. With your betsize, the pot on the river is $2.20, and you have $3.45 left behind. If he checks again, you have to overbet to get all in.

3) Shove the river every time. AA, A6, and 33 are the only hands in the entire deck that beat us.