Most Canon cameras can be controlled using CHDK , (Canon Hack Development Kit) a great Open Source project.

Start with an dirt cheap Esky 8g (8 gram) servo.
This one was labeled ESRV0A others are ES070A, but most of them are the same, and many other similar servos will work as well.

This is the disassembled servo, observe the three wires that go to the potentiometer. 
The potentiometer is the part that defines when the servo is satisfied with it's position at a given stick input.



You want to remove it, and solder two equal resistors, in the 1K-5Kohm range, disregard the 10K resistors in the picture, an 1kOhm resistor is marked "102" , if you don't have SMD prts, it's OK to use any other resistors.  Or you can just epoxy the existing potentiometer so I't's stuck in the middle.


And this is how it looks when it's done, one of the leads to the motor+GND will deliver about 4volt to the USB connector of the camera, this is enough for the camera to sense input, and act.



With a total length of 35cm, and USB connector + shrinktube, the whole device weights only 3,3gram !

Final tip:  The micro-USB connector is the contents on an common USB connector, I just cut off the black plastic cover, and epoxied the whole thing.