Stepper Motor Inconsistancies

Go info. So I think my solution is a different question.

Using the Arduino Uno and Arduino motor shield. What kind of stepper motor can I use to pull 6 lbs. The goal is to fairly accurately raise it to different levels. It's currently able to pull the weight up about 1/2 the needed distance. This is for a one day activity, crude, not intended to run more than a few hours so nothing to fancy/expensive.

Any ideas?