This is a scary flop, against one opponent I might CB but against 2 a check is fine. On the turn you need to bet every time, the SB has now checked twice, most people don't check a 2nd time with a Q the only person that I have to worry about is the button. On this turn the only real hands that should scare you are a Q and KT, your hand is now pretty strong you need to bet and get value from a lesser ace. As played I guess I check the river too since you didn't protect your hand on the turn you now really cant try to get any kind of value out of the hand on the river.

So is it fine that I didn't play a big pot here? When your saying bet the turn about how much would be a good amount? During the hand, I was contemplating between 1/2 & 2/3 pot, would that have been good? Also if the river was a blank, how much would i bet there?

It really depends on the action but in general no its not a hand where you want to play a big pot but that doesn't mean your cant extract value. If you bet the turn and get raised you are going to fold most of the time, but there is a good chance you can get a call from another ace on both the turn and river and get value out of the hand. On the turn a 1/2 to 2/3 pot bet seems good.