What could be reason that people with aids are so skinny?

Several: Infections may involve the gut and cause malabsorption. Advanced aids makes a person feel terrible and perhaps not want to eat. The virus if present in large quantities can cause apoptosis of skeletal muscle. There are probably other reasons.

Misinformed: I appreciate the question, but in general there are some assumptions here that are just not reality. Most people today with HIV infection never get immune system destruction and do not get aids. And, most people who did get aids no longer qualify for that with full immune system recovery. In fact most people with HIV no longer have any physical sign of infection and their bodies look normal.