Should wilson's disease patients use weight-gaining supplements to help maintain their weight?  

Not really. Patients should consume only in moderation foods that contain high concentrations of copper (shellfish, nuts, chocolate, mushrooms, and organ meats), particularly during the first year of therapy. Weight gaining suppliments sold in health food stores are poorly monitored and their contents are unpredictable. Suppliments such as ensure or boost may be ok so long as there copper content is low.
Just stay fit. In our world, with abundant great-tasting food, there's no need to "maintain your weight" with supplements unless your profession requires extreme prolonged aerobic exertion. Wilson's patients are like everyone else in that aerobic exercise helps set your appetite so you maintain good musculature with relatively little fat, which is right for almost everyone.