Weight refers to the stroke thickness of each typeface (Williams). You are probably familiar with setting type to bold from the command menu on a word processing program. What happens when you use the bold command is that you are increasing that type's weight. Again, if you are going to increase a types weight, make sure you make it obvious(1). It will look more like a mistake if the difference is subtle. This will definitely add more interest to a page that is otherwise well organized and laid out(2-3).
