From what I understand, Ozzy doubles each phrase as he sings it. In other words, he sings a line or a half a line, stops, then doubles it.
That may be because he can't remember much more than a line at a time...
Seriously, Ozzy sounds pretty good for a guy who's put himself thru the ringer.
Double/triple tracking phrases is common place with background vocals.
That's how you get that nice stereo spread... where the parts take on an "ensemble" (rather than solo) character.
Key lines are also commonly doubled on the lead vocal, but it's usually tucked a bit under the main track.
All that said, (at the risk of repeating) I'd first make sure I'm getting a nice/full sound from the mic.
If that's not happening, the solution isn't in processing/treatment... but rather chosing a different mic.
Note that there are very affordable decent mic options today. MCA-SP1 and the B3 are but two examples