It's a difficult one isn't it, you have a very old lady here who obviously needs the dog for company and dotes on it, so it feels very cruel to report her again to the RSPCA, (which is what needs to be done really if she will not help the dog) but then you have a dog who is slowly being led to an early death and your having to watch it yourself.

If you push too hard she will probably just avoid you and think it is none of your business, so try to keep smiling and keep it light, no-one likes to feel they are not in control of their life having others telling them what to do, because we all know that to save this dog it will probably need re-homing, she can't give it the right exercise and she is unlikely to want to put the dog on rations to get it's weight down as with many they see giving their dog treats and food an extension of loving them, no doubt she will feel 'cruel' in not giving her dog these terrible foods, so I don't hold out much hope unless she is faced with loosing the dog forever if she doesn't.
She hasn't taken her vets advice, I doubt very much that she will take yours and may well be offended. Your correct the rescue should never have given a Collie type dog to a lady who can not walk enough, a young Collie constantly on a lead, doing slow walks, poor thing, no life for it. Perhaps you could suggest ball retrieve games in her garden to help exercise the dog much more, that would help a lot, and the dog could get quite a lot of exercise that way.

By all means you can try to print off information for her and hope she will take it from you in good faith.
I've also added on this link for you to copy out for her, with regards to chocolate and if she is also giving cake with raisins in it etc for her to read, I chose this one as it has a vets verification so
may hit home.
http://dog-care.suite101.com/article.cfm/dangers_of_chocolate_for_dogsTo be honest her vet is likely to report her if the dog is becoming obese and unhealthy they have a duty to do this now. It would be very sad for the lady to loose her dog, do what you can, but don't expect too much, people often don't wish to listen.