The last big step was building the weight. I purchased two lead diving weights and hung it to the throwing arm with a piece of leather belt and metal plates cut from the same bicycle chainguard as the sling release pin.
I cut the belt and attached the metal plates to it, estimated the height of the weight from the bottom to the upper fastening holes and subtracted that amount from the distance between the axle and the base. Then I subtracted a few centimeters (just to be safe) to get the distance between the weight fastening holes and the axle.
You absolutely DO NOT want to MELT LEAD! http://en.wikipedia.org/wiki/Lead#Health_effects