All disc problems are not alike. Some are bulging discs. Some are ruptured discs. The best way you will know what exercises are safe for your back is to have physical therapy.
Your therapist will evaluate your back and symptoms. They will correct muscle imbalances, soft-tissue and joint restrictions, and teach you corrective exercises as well as self treatment techniques including self mobilization and/or traction, or heat/ice to control symptoms. Once you have some control over your symptoms, they will help you establish a safe exercise program which may include:
- Walking (with or without nordic walking poles, or walking/exercising in water)
- Cycling - If you can't tolerate walking, cycling or using a recumbent cycle can allow you to burn calories.
- Strengthening - Safe ways to include strength training such as the ball wall squat with the ball giving the back support, using resistance bands, or other ways to support your back when lifting weight.
- Stretching - Tight muscles in the hips and legs can increase the strain on your back, so your therapist can give you appropriate stretches with the proper modifications.
When looking for a therapist, ask questions to make sure that you are getting one who specializes
in backs and who will help you establish a good long term exercise program. I think you will find that you will get the best results with professional help. Otherwise you will have a lot of trial and error.
Also to reduce weight be sure to adjust your intake to your activity levels. Good luck. Hope that helps.