As far as I'm concerned a belt is just something that holds your pants up. It might not be that way to everyone though - maybe he's hanging it up on his wall at home and using it for inspiration. Maybe he's giving it to a friend that lost theirs. If it bothers you that much, just ask him. I, personally, don't see what the big deal is, as long as he's not wearing it to class or trying to act like a bigshot.
Exactly a belt by itself is meaningless even a black one. It's what you have to do to earn it that counts.
He could have legitimate reasons for buying this belt or he may just want to show off, either way as long as he doesn't wear it in class until he's earnt it I don't see a problem. Especially as I could order any belt I liked off or internet or for a shop for that matter.
A yellow belt at 1 class can be worth more than a brown at another the requirements vary from place to place.