* could it be as simple as he's getting a good night's sleep on weekend nights, goes to school well rested on Monday morning, then doesn't get the same type of quality sleep during the week so it catches up with him by the middle-end of the week?
This was definitely going on with our DD a *lot* when she was 7 and 8; now that she's 9, we aren't noticing it as much. She usually has trouble getting to sleep (wants to read instead) and it was definitely catching up with her during the week--by Friday afternoon, she was usually literally falling asleep in her after-school music class and had tremendous difficulty concentrating and behaving. Now it seems better, but I'm not sure what made the difference--we tried all kinds of things to get her to sleep before and nothing really worked well.
But as polarbear says, it's hard to know. Good luck to your friend!