Smaller pre. 2.5x is standard from the CO. You're just trying to steal the blinds from late position usually. I don't mind going bigger at low stakes if it's appropriate. But A3 is not a particularly good hand.
Flop is bigger than it needs to be. 1/3 pot is making almost all the same hands fold. We're in a less awkward spot if we get raised.
Turn you could bet or check. One argument for checking is that a lot of his range already folded the flop - it's a difficult board to hit. There are some questions about what is actually folding the turn. Barreling is totally fine though.
River you check back and lose
. A queen is simply not folding very often. Betting again is throwing away a lot of big blinds for nothing.