What type of sensor could I use to determine the mass of a small object (under 1 kg)?
Just a little brainstorming:

If you have a spring, then you can easily calculate the physical force (mass) needed to stretch the spring to a certain extent. The law is called:
 Hookes's Law
 - you could then just measure the increase in distance between the initial position and the position with load. Use a servo or any distance measure.