Time Machine does not fully backup libraries

I use Time Machine, but am finding that, even though in my Preferences NO files are excluded, TM does not fully backup the libraries.

Some is missing from the main Library, some from the System Library, and a huge chunk (over 2GB) is missing from the User Library.

So I can't use Time Machine for restores!!!

Does anyone know why TM is not fully bupping libraries and what I can do about it?

thanks