Hypothyroidism is not a symtom of Interferons....so, that wouldnt make sense. Avonex being the same drug as Rebif, Im sitting here reading the package insert and see no warnings about weight gain whatsoever.....you should probably talk to your doctor about that.
Of course STRESS can certainly cause weight gain, and if you recently started Avonex, or are recently diagnosed, learning how to do your shots, that would certainly explain it! Nothing more stressful then that!
But honestly, I would speak to your doctor. Its possible that your body isnt tolerating Avonex and you need to consider a med change. Elevated Liver Enzymes would be the only Organ Change that Interferons normally can affect...but those dont cause weight gain. So, give your doc a call if you are experinecing problems which you cant explain.