Hi there

Hopefully someone can help me with this hand. I play 10NL (doing ok, but there's much to learn...), building my roll for 25NL. I'm often quite unsure how to play overcards, especially against opps who tend to call a lot.

Sadly, Everest Poker is not recognized by the FTR HH converter, but I hope I made the log readable:

UTG+1 is at seat 0 with $1.75.
UTG+2 is at seat 1 with $20.70.
MP1 is at seat 2 with $3.01.
MP2 is at seat 3 with $15.42.
MP3 is at seat 4 with $10.90.
HERO is at seat 5 with $12.28.
Button is at seat 6 with $9.90.
SB is at seat 7 with $8.31.
BB is at seat 8 with $2.07.
UTG is at seat 9 with $5.51.

SB posts a blind of $.05.
BB posts a blind of $.10.

(HERO is dealt Ad Qd.)

Pre-flop:
UTG folds.
UTG+1 folds.
UTG+2 folds.
MP1 calls for $.10.
MP2 folds.
MP3 folds.
HERO raises $.35.
Button calls for $.45.
SB calls for $.40.
BB folds.
MP1 folds.

The flop comes ($1.47)
3h 2d 7s.

SB checks.
HERO bets $.80.
Button calls for $.80.
SB folds.

The turn comes 10d. ($3.18)

HERO bets $1.20.
Button calls for $1.20.

The river comes 8c.

HERO checks.
Button bets $5.55.
HERO folds.

Was the bet on turn too small? Or would you rather not have 2nd barrelled here? I wanted to see the river as cheap as possible
Checking the river was probably not too smart, too, but then I had no reason not to believe I was 2nd on river?