my mum is overweight but does not want to lose weight

My mum is overweight but does not want to lose weight and she has a really bad backand sore feet what can I do?

If she doesn't want to do anything about her weight it will be bit difficult to convince her but you can still try and encourage her. I think you have to find a way to tell (and convince) her how important it is to you without being insensitive or pushy. For example, when she complains about how bad her back is, you could say I was told that swimming was really good for back pain, maybe we could go swimming together this weekend? That way you could convince her to do some exercise while also accompanying her. By the way, Swimming is one of the best ways to exercise and is really good for people who are overweight because there isn't so much pressure on their joints and back.
If you can't get her into a bathing suit then try stretching exercises (for the back, yoga is really good) and do them with her. Tell her that it makes you sad to see her in pain and that you want to help her. And the easiest exercise of all is talking a walk. Try to get a routine where you and your Mom go for regular walks together around the neighborhood.
As for healthy eating, well you could lead the example by making healthy food for supper and helping her make better food choices. Ex.: Salade, steamed vegetables with rice with fruit salade for desert.
Hope this helps a bit!

just convince her to eat heath and exercise and tell her that you love her and care for her and give her a hug that shows how much you care

You can't help someone that doesn't want to help themselves. You can choose to not support her unhealthy habits. She will have to want to make that change for herself.