I agree the Edge is awful, you did ask for a 10 mt match rifle, the 200 although quite light but is not a 10 mt match rifle although it is an excellent Sporter class target rifle, a class also shot at 10 mts but it has a heavier trigger.
The only true light 10 mt match rifle available now is the Walther LG300 Junior which in its standard form is under 3.5 kg. When my wife returned to shooting after many years away she bought one as the compact dimensions suit the smaller frame but she did immediately add a kilo of weight to it! She still uses the stock but we have now put a LG400 action into it. We also have one as a club rifle and it is ideal for new shooters wanting a light rifle.
Weight should also not impact on a back injury as the position should not be held on muscles but supported by triangulation of the skeleton. The general shape of the position may impact a back problem and this would be regardless of the rifle weight. I would advise you get assistance from a good coach as the position and particularly a bad position is far more likely to exaserbate your back injury.
Best of luck and good shooting,
Robin