1.) emphasis of important elements in the picture. thicker lines help bring attention to those forms. This is especially useful here, as the figures quickly become lost in the complex lineart. Here, the thicker outline of the ice sprite makes it more visible over the lines used for the magical energy surrounding it. details such as the inside of the ear and the speculars on the forehead are also less important and therefore have a thinner outline.

NOTE: while outlining in thick line helps to emphasize the form, avoid "cookie cutter" lines, where ONLY the outer line is thickened. allow the thickness of the outline to insert into the interior of the form, like at the ice sprite's hairline: the outer line (red) inserts into the hairline (blue).

2.) more 'dynamic' lines. varying the line thickness along the same line can give the illusion of motion and movement... Here, as the folds of the cape moves down and to the right, the line thickness increases, making it look like it's flowing to the right.

3.) illusion of perspective. Aside from the obvious size difference, the distance between the mage's two hands is shown by the line thickness; in general things closer to the viewer have thicker lines, things farther away have thinner ones.

4.) tweaking of the lineart. As we all know, it's easy to make mistakes with a single line. And there are no undos (UNDO! UNDO! ...ahh.)...line width thickness allows you to smooth over any (minor) mistakes that might come up while inking the first time around. Also, even if there aren't any mistakes, it still allows you to subtly alter the lineart, if you so wish. Here, I later decided to soften the sharp edge along the tail of the ice sprite...not to mention it was looking a little knobby...

5.) shadow/cast shadow elements. In the case where you want the shadow or cast shadow to be totally black, the outline can be altered to suggest shadow. Note how the shadow cast by the sleeve follows the contours of the cloth that it is cast on (red arrow) while the shadow cast by the necklace suggests the shape of the necklace (blue arrow).