A person’s body weight can put a stress on the joints and back; the heavier the weight, the more the stress. People who are not heavy can hurt their back just by bending the wrong way, picking a piece of paper off the floor, for example. It’s not the paper that was heavy, it was the upper body.
It is possible that your back injury is new and is being aggravated by your body weight. Perhaps your doctor feels that if your weight decreases, the strain on your back will decrease as well.
When you have questions like this, it’s always best to speak to your doctor so you can get a better understanding of the reasoning.