Are there ways around this issue?
Larger weight, smaller diameter (e.g. around workpiece in picture).
Reset weight to next jaw after 120 degrees of rotation.
Use tautline (or any friction) hitch on line and reset after each index (similar to adjusting the guyline on a tent).
Bungee cord pulling horizontally (technically not constant force).
Tie dog to chuck and put bone 14″ from its jaws.
There are not so many lathes that would be within less than 12″ of the floor. You only need drill a hole in the bench the diameter of the string.