My current theory about my observations with my scales is as follows:
The pile, although thin, on my carpet can be felt to move slightly sideways when pressed with a finger. My scales have 4 feet and on the carpet the body of the scales is supported only by the 4 feet, not by the body itself (paper can be slid underneath). When the 4 feet press on the carpet, the downward force resolves into the vertical force and the force sideways to deform the carpet. The scales are measuring the downward force via the feet and not the sideways force, hence the much lower reading on carpet than on the flat surface.
Whether this is right or wrong, I am now happy that I think I understand the effect. Tiny pointy feet or my tile under the scales making them accurate seem to fit with this theory.