He is obviously depressed. Many mental problems are caused by a poor diet and bad habits. And his junk food diet seems to be the cause. The first things that need to change are his sleep schedule, and his diet. And finally, everyone in that house has been too soft on him his entire life, probably because he is the "little" brother. It is time for some tough love.

So sleep schedule (rise with the sun), diet (proper macronutrients and micronutrients), and tough love. Once he gets his energy back, an exercise program would be the most beneficial. He needs to turn his life around and you need to help him see that it is very possible. I would call him and have a serious talk about becoming a man. And make him see that he is at a very serious crossroad in life that he can either overcome or fail. He should see this as a challenge.

All of this will take time. Small incremental steps, daily, are the only way. Start with two things: 1 - Wake up 1 hour earlier everyday for a week (and 1 hour earlier than that the following weeks until he adjusts to a proper waking hour. If 1 hour becomes too much, then 30 minutes earlier. But the main thing is progress however small). 2 - Eat a healthy breakfast everyday. Eat the same thing everyday. Something simple to put together that does not take much time or preparation. Make it something that he likes. Include salt. That is fine. As long as it is not junk food. Along with this first meal, take at least 4000-8000iu of vitamin D3.

I make specific note to vitamin D3 because it is probably the most essential vitamin when it comes to mood and hormonal activity. Your brother, I am almost certain, has a vitamin D3 deficiency.

So, ultimately, have a serious talk with him. Show him concern and that you have high hopes for him and he needs to start practicing becoming a man. Get him to work on creating a consistent sleep schedule, and a healthier diet.