Are you in engineering? I'm a 4th year mechanical myself at the University of Saskatchewan.
I agree with you there, that property is called hysteresis (sp?) I believe. Learned some about that in hydraulics since it affects how relief valves (and other things with springs) open and close with pressure. However, I think you could still set the band to have the same linear effect either way. You would just have to have a little more pretension when using it in the unloading direction. (band is lifting the weight). Anyways, I didn't think the hysteresis of the band would be a large enough effect to consider but I've also never tried it before!