I too have back problems riding my bike. The muscles in my lower back start to burn and ache and I have to stand up and stretch all the time while riding. During the winter months I ride the same bike in the same position indoors on a trainer - and I never have ANY back pain. But as soon as I go out on the road, it starts again, after about 30 minutes or so. I think the difference is that I am balancing as well as riding, which you don´t on a fixed trainer indoors. Even though it´s the same bike.
Part from getting a really good bike fit, I have been told to train my core muscles. Doing the "plank" is one way - but I can only hold it for less than 30 seconds yet, it´s quite a tough one. You can do the usual Plank and the Side Plank. All to strengthen you core muscles.
As far as weight loss goes, i found a neat way during my recent weight loss: I change all pasta, rice and potatoes for bags of frozen veg. You can find all sorts of mixed veg in the freezer department, and they are usually a tiny 20 - 35 calories per 100 grams, so a whole 500 gram bag gives you maybe 150 calories! But it sure fills you up, it is good for you and some of the mixes tast really good. On top of them I put whatever the rest of the family eats - a ladle of tomatoe sauce, curry sauce or whatever. (I don´t fry the veg in much oil, if any, I use a good non stick pan. Maybe some soy sauce to spiff it up a bit.)
Good luck on your inspiring journey!