I'm on meds and haven't had issues with weight. In my case when I'm depressed I kind of don't move. So being not depressed also means exercising and sports and other things. If there's any weight issue it must be balanced out by that.
One note about anxiety in the first month... my doctor told me that this can often happen when you're just starting on a med. She said that for some people you get your energy back before the mood stabilizing effects kick in, so it feels temporarily that things have gotten worse.