Betsize on the river

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Betsize on the river

Blinds: $0.01/$0.02 (6 Players) BN: $4.28
SB: $2.70
BB: $2.50 (Hero)
UTG: $2.53
MP: $2.34
CO: $1.97
Preflop ($0.03) Hero is BB with Q Q
UTG folds, MP raises to $0.06, 3 folds, Hero raises to $0.21, MP raises to $0.52, Hero calls $0.31
Opponent is 30/25 with 14.3 3bet (unfortunately no 4b stats) on ca 100 hands and high AF. Guess a fold would be way too tight, call might be okay if I knew that he raise/folds too much.
Flop ($1.05) 4 Q 3
Hero checks, MP bets $0.53, Hero calls $0.53
Flop is as good as it gets, given his AF I think the x-call is standard.
Turn ($2.11) 4 Q 3 4
Hero checks, MP checks
Plan to xc turn and x/shove rvr.
River ($2.11) 4 Q 3 4 9
Hero bets $0.88, MP calls $0.88
He has ca 60BB left and I wasn't sure what to bet. I think the play is just betting all-in. Him slowing down on the turn gives me reason think that he has sd-value or trying to catch 3-6 outs. While I think that my play was probably not the highest EV, during play I was thinking I could get some more crying calls if I bet a size that makes bluffing cheaper from my point of view.
What are your thoughts?

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