it would not. I think lens weigh comes entirely from the design and speed of the lens. The designs don't vary that much so I would t consider it. Take the full frame canon 70-200 f4, it weighs 760g, vs the 1.5 crop fuji 50-140 f2.8 which weighs 995g. They are nearly identical in aperture size and focal length, and will produce similar looking images for comparisons sake. All that to say, the amount of glass used is what will determine the size and weight of a lens, not the sensor size. There are many other factors but in general for crop bs full frame there is little difference.