I think Dan is probably right about the normal working range being broadly linear, but it certainly isn't linear on the way there. I.E. I would expect (much) more stretch going from 0-50kg than 50-100kg. And likewise progressively less as loads increase beyond that.
As an aside, the most interesting piece of research I've seen in recent years was on cutting resistance vs load. That relationship has generally been assumed to be broadly linear, but isn't at all - ropes under high tension lose almost all resistance to cutting. It makes a strong argument for placing an absolute limit on any tension loads for hauling or rigging, and ensuring if falls are possible the rope is well away from any hazards at the moment of peak force. Not always easy in rock climbing....