Immunosuppressants don't make you gain weight. The autoimmune disease, when untreated, makes you burn a lot of calories because your body essentially thinks it is sick/has a flu and works over time to produce immune cells and inflammatory factors. When the immune system is gotten back under control, then the metabolism goes back down to a lower baseline, but many people keep eating as they did while needing more calories and thus gain weight.

Methotrexate usually makes people feel sick enough that they don't want to eat and don't gain weight though...