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Losing weight and exercising can be beneficial for your back as well as your overall health. We don't know the specifics of your back problems (or your health) so we cannot recommend any specific exercise programs. But your doctor can. Low impact aerobic activity is usually well tolerated for people with back problems such as walking (if able to walk) or cycling on a stationary bike. There are exercises that one can do sitting down, helpful for those that are wheelchair bound. Discuss your options with your doctor. Below are some resources that may help. Copy/paste the links.
Exercise and Back Pain:
How to Exercise if You Have Limited Mobility: