Your brother sounds just like my oldest son. The doctor told me that they call the dark circles "allergy shiners" those and the eczema are probably allergy related. My son also has asthma and adhd (some of my sons adhd meds made his dark circles worse). Make sure he gets plenty of vitamin d3, b vitamins and omega 3's. My son has outgrown his asthma and allergies, but he's still lazy.
It is possible that it is parasite related. It wouldn't hurt to get him checked either way.