I dealt with my back occasionally "going out" entirely for years, to the point where I couldn't leave my bed for a day or more. I was able to correct this through isometric exercises, specifically "planking" (or "plank pose"), to build core muscles, protecting my spine.
I suggest using the front, back, and side poses in which you rest on your elbows. This keeps you closer to the floor. This way, when your muscles give out (and they will) you'll be able to bring yourself down gently.
Once you become familiar with the feeling of activating your core muscle groups, you can do a lighter form of the same exercise while walking, sitting, or simply standing. In fact, engaging your core muscles is essential to avoiding injury during other exercises, and planks are a great way to make a habit of it.
Exercise aside, I'm probably not telling you anything you haven't heard before, but examine your diet and see what can be adjusted. More and more, my diet looks like Dave Asprey's Bulletproof Diet, and I've never felt better.
Best of luck!
And lifting/barbells for body/core strength; https://www.youtube.com/user/athrall7
As neverminder mentioned, form is critical and take it slow until you build strength. I do benchpress, overhead press, squats and deadlift every other day and I am in/out of the gym in an hour. I've had two cervical fusion surgeries and found that typical Rx of pills, back braces, bed rest, take it easy (i.e. become sedentary), etc. just make things worse because they weaken the structure.
What appeals to me about the method is that it's based on solid thinking about the physics and physiology involved. The book is full of anatomical drawings that wouldn't be necessary and wouldn't be found in your average workout book. The creator really made a thorough study of strength training his life's work.
For the longer term, work on building up ab strength, which takes the load off your back muscles a bit. Those of us who sit all day long tend to have very weak abs.
You might want to book an appointment or two with a physical therapist - not ongoing weekly treatments, but they should be able to show you exercises that are safe at your current level of conditioning and make sure you're using proper form. Without those two things, you run the risk of exacerbating your existing injury or causing a new, worse one.
1) You almost certainly won't lose weight without changing your diet.
2) Heavy weight exercise is great for lots of things, but if your lower back is hurting it could also be you aren't limber enough in your lower back and upper legs. Stretching for your glutes/hamstrings/IT bands etc may provide more immediate relief.
See the book "Treat your own back"
When I injured my back 20 years ago I found them quite helpful in recuperating.