My guess is that your lens are dirty, and playing lots of burned discs force it further. My Wii stopped reading discs too, and I'm pretty sure it's a lens problem. I've ordered the Wii Lens Cleaning Kit to solve the problem.. Dunno if it'll work, but if it does, I'll post here.
By the way, my original games don't work, not only backups. I don't know if that happens to you too.