The fat lines are called strokes and the thickness of that line is called the stroke weight. When working in any illustration program Adobe, Flexi, Corel, you will need to convert the stroke to outlines if you are going to perform and cut function.
This is also a rule when subbing out work to the big printing companies.
Fonts to outlines, Strokes to paths.
I am attaching a screen shot of a flange, and I have set a stroke weight of .01 on the grey for illustration purposes Only. The CNC file will not have any stroke weight.
Hope this helps.
Cheers