FLOPPED SET DEUCES TURNED FULL HOUSE. IS GOING ALL-IN TOO MUCH?

Here we have a family pot pre-flop with it only costing me a $1 to see the flop with pockets 2s.  I flopped a set with an ace and king on board and make a pot sized bet into the entire table.  I get one caller and then the turn is another Ace giving me a full house.  I bet $40 and get called.  I put my opponent on an Ace for three aces or King since there were no draws present and if they have AK I would have heard from them already pre or post flop. With a river blank I move all-in for a pot sized bet and he folds.  Should I have made a reasonable half pot bet to extract more value from opponent or put them to a decision for their all-in at the end?  I always feel like I bet too much and scare my opponents away when I have them on the ropes with a killer hand. Thanks. Gil