Hmmm.  Helpful but not quite what I'm seeking.

I'll try to rephrase my original question:

I can draw a line in Anime Studio Pro.  In the Fill tool panel is a tool called "Line Width (W)".  

I can select that tool, place it over one point of the line/path just drawn, and vary the width of that point.

That's what I'm trying to do.

Take a look at Supergirls eye lashes:
http://www.renderosity.com/mod/gallery/index.php?image_id=1359637&member

They are wide at the base at the eye lid and extend to a sharp point.  

I can create that effect in Anime Studio Pro with the Line Width tool using only a single stroke.

Does Adobe Illustrator have a similar tool?