Use a 360° servo as a motor and a coupling from Servo City; selected by the servo mfg you select and the size of screw you wish to use. Get the screw long enough the there is some un-threaded shaft at the head, cut off the head and use that to fit into the coupling. You'll need some sort of guide/rail to keep the weight from spinning and guide its travel. You might consider using a lighter weight and moving it further, giving you a more finite adjustment.