I thought I should share in case anyone else has this problem.
Creating a graphic for an animation, I used the pencil tool and made my lines. Went to the width tool to alter them and nothing. A little circle with a line through it indicated that I could not change the line.
After an hour of time wasted on this and plenty of expletives later I figured it out.
Select the line you want to use with the Width Tool (or all of them if you are planning on using the Width Tool on all of them).
Go to the brushes panel (should be on the top bar) and click Remove Brush Stroke (Looks like a little paint brush with a line through it).
It seems to have fixed the problem.
The Wyrd One