turn the nuts, river overbet?

[daven]

co is 16-12-4 reg with 60% fold to cbet and likes to mix it up
bu is 55-5 whale who doesn't fold much (30% fold to cbet) and will only raise the nuts

I don't c-bet cos i'm about 70-30 here = sometimes i do, sometimes i don't. These guys aren't going anywhere, but I do have a bunch of equity vs their calling ranges so obviously a c-bet isn't bad. Turn and I hit the nuts so i have to start trying to get money in - I hate my sizing. River is cool cos it gives the whale so many two pair ++ hands, overbet shove for lols? Apply 3-button theory and bet $26? (= he has 3 buttons to choose from, fold, call, raise - so he has 2/3 chances to go retardo, instead of 1/2)

Full Tilt No-Limit Hold'em, $0.25 BB (9 handed) - Full-Tilt Converter Tool from FlopTurnRiver.com

MP3 ($40.86)
CO ($17.50)
Button ($52.27)
SB ($25)
BB ($25)
UTG ($25)
UTG+1 ($25.77)
Hero (MP1) ($30.16)
MP2 ($9.54)

Preflop: Hero is MP1 with 3, A
2 folds, Hero bets $1.10, 1 fold, MP3 calls $1.10, 1 fold, Button calls $1.10, 2 folds

Flop: ($3.90) 9, 2, 7 (3 players)
Hero checks, MP3 checks, Button checks

Turn: ($3.90) 10 (3 players)
Hero bets $2.80, 1 fold, Button calls $2.80

River: ($9.50) J (2 players)
Hero bets $?? ,