I can lose weight on an 800 calorie, protein and salad only diet. I can lose weight on a sensible 1200 calorie diet--as long as there are no carbs in it. The moment I add 1 slice of whole wheat bread, piece of fruit, or bowl of oatmeal, I gain 5 pounds. Nobody can eat like that forever. Nobody should. All the vitamin pills in the world won't supply the nutrients you aren't ingesting. The charts say I'm overweight, but when I was at my "perfect" weight, my bones stuck out. My shoulders, hips, and ribs are size 16, not size 10. And, guess what? I hurt more when I was skinny. The brain fog was awful. My skin got sallow and lifeless from lack of fat and its vitamin A. The insomnia and fatigue were already so bad I didn't believe they could get worse, but they did.
Arthritic hips and knees don't like extra weight. Fibromyalgia doesn't care what you weigh. If you have arthritic joints, losing weight is worth a try. If your pain is muscular, or in your tendons and ligaments (mine is at the attachment points, not the belly of each muscle) losing weight is something that you should consider if you have other weight-related health issues. But don't expect your fibromyalgia to melt away with those pounds. It probably won't.