It does both. I haven't really watched my weight while doing Insanity but you will see results in two months if you manage to really stick to it and eat good. I'm doing it second time now, however I'm not sticking to it as much as I did in first time, since it's spring I can go ride a bike, play basketball or football, I still do it once or twice a week.
Again, important thing is to be consistent with it and eat well.
What you eat can have a direct effect on your skin if you're struggling with psoriasis. See what to shop for.