I would have bet atleast $5 on the flop.

The less then half pot bet screams "I dont know where I stand"

I like the suggestion of a pot bet is good here.

A solid bet like that OOP, shows strength. Id consider playing back at the $3 with AK in position here, but $7 I quickly decide to not mess around. Wouldnt seem likely a raise would get me anything but trouble.