One thing that bothers me is that you haven't said how much it can lift as it is. I think testing the current arm is the first step. How much can it lift when fully extended? by moving each joint?
Matts suggestion of a counter weight is a very good one. The only downside is that rotation of the base will be more difficult. A more difficult but better solution would be to move the "elbow" motor back just behind the "sholder" gear, turned 90' with a shaft extension coupled to it, to take the motion back to the worm gear drive at the elbow. That both reduces the hung weight and uses the motor as the counter ballance. It would require: 1) a new mounting bracket for the motor, 2) the shaft extension and couplers 3) a new mount for the drive gear in the elbow worm gear.
A larger motor at the shoulder might help, but I think a worm gear with a finer pitch would make more of a difference. The motion would be slower, but stronger. As noted, friction would increase, but I think it would still be worth trying. The other option is a gear box between the motor and the worm gear, but the problem there is that it introduces additional slop and friction. Replacing the worm gear with a gear box is probably best, but the most difficult.
I do hope you will keep us in the loop and show us what changes you make and how it changes the design.
James hosts the single best wiki page about steppers for CNC hobbyists on the net:
http://www.piclist.com/techref/io/steppers.htm Disagree? Tell him what's missing! ,o)