I agree 100% with your post. However to the OP I would say you are getting tied up in knots over just a few kilos. A decent modern bike is about 68-70Kg and the Mechatechno is 60Kg and (I think) the lightest option of all. Unless the bike falls on top of you you will not really notice much difference. If you have a bad back it will be technique and skill that will have the biggest effect, not the weight of the bike. Most people, for example, when they first start try to pull up the bars to lift the front wheel and that can stress the back muscles. Once you learn to let the engine and clutch do the work it is no stress at all.
Try to get a ride on a good 250 and I think you will be pleasantly surprised. But yes a 125 is a good bike if you can pick up a good one. Much easier to find a 250 that has had an easy life. If you can afford it and buy new the Mechatechno (10 grand) is an amazing thing, my missus has an electric (EM) and they are really, really good. If money were no object that (Mechatecno) would be my choice.