Load cell is actually a strain gauge attached to a beam, in such a way as to measure the elastic deformation of the beam under load. A higher load will accelerate the effects of creep, which will be one of the modes of long term reading drift. Affects like work-hardening, corrosion and fatigue will also be there.
My working assumption is that those effects are going to make long term readings from a constantly loaded load-cell drift in such a way that you can't really trust the reading you get, until you, at least, re-tare the load cell to a known load. If you can prove I'm crazy, that would be great.