I can tell you that I gained weight with my burning mouth, since mine's apparently nerve related (lesion caused by MS), and I got relief from eating. The burning was gone as I ate food.I am now losing the weight that I put on by having healthy alternatives around, such as carrots and celery. Lots of fat free foods as well. Lots of gum to chew which gives me relief.
I'm not sure what drugs you are taking in your case, but I am taking Neurotin (600mg daily) and Amitriptyline (10mg at night) for mine. I find they're helping a bit (before it was so bad it kept me awake at night, now on a good day I can still feel the burning, but it's minimal, a bad day I can at least sleep despite the burning).
Diagnosed MS 03/08 Relapsing/Remitting.