Sigma already have a 150-600 f/6.3. A f/5.6 version would only be a little larger - not 60-70%. Sacrificing a little at the short end - 200-600 - would allow you to save a little weight and gain some image quality. Canon also already have a 200-560mm f/4-5.6 - 200-600 would only be marginally larger, and not necessarily heavier, depending on materials chosen. And, as a high-end supertelephoto, you're likely to be using it on a monopod or gimbal mount most of the time anyway.
It would be 60-70% heavier if it were built to the same standards, using similar optical construction. It would need be physically 20% larger in very dimension, and that converts to 1.2^3 in mass and weight. The 200-500 is already a plastic lens. There doesn't seem to be much room to reduce weight using lighter materials unless one makes it flimsy as well.
Canon's 200-400f/4, extendable to 5605/5.6, is in fact weigh 70% more than Nikon's 200-500, and it doesn't even get to 600mm
In fact the 200-500 itself, despite the smaller zoom ratio and smaller aperture on the short end, is 60-70% heavier than Nikon's own already portly 80-400.
A 200-600f/5.6 clearly would not be a lens in the same class of portability and usability as the 200-500f/5.6. It would be a specialty lens, probably not good enough for people who really need 600mm, and way to heavy for people who just want 600mm.