I think the flop raise is actually too big. $3.5-$4 is fine.

I also bet much less on the turn. You run the risk of moving a bad Ace out of the pot.

If you raise the flop to $4, the pot will have $11 on the turn. Bet $8 on the turn, the pot has $27 on the river, bet $20-22 on the river or whatever he has left.