If the range is small, add 2 springs in tension, pulling up, to take some of the load. Set them pointing outward at 45deg or so, so that they give a gentle pull all the way through the range. Either do some maths, or use trial and error. Important thing is:
Springs do not go slack at top
Springs do not go so tight at the bottom that there is more load on the leadscrew than there would have been without them

This will also reduce self wind (rhymes with mind not thinned!)

Set it so that without the leadscrew connected the load hangs about halfway down. Then add the leadscrew and motor. This is a bit like an industrial assist, sometimes called zero g assist. Some Z axis routers (mechmate??) use this idea.