
I might be digging up old posts but here's my input on line weight. (pardon me for I've been taking too many art classes)
Line weight gives your art depth, body, weight and interest. It can also "trick" the eye of your viewer. For instance the photo to the right of this text was drawn with nothing but straight lines and yet your eye perceives some of lines as curved. Why? Line weight (I say some because I got lazy halfway through drawing the stupid picture) Anyway, to put it another way think of how much more fluid calligraphic text looks to text like this? Calligraphic text is always more interesting because of line weight.
As far as drawing it, the closer something is the thicker the line. Also in most comicing the middle of the stroke is thicker than the ends (not by much in this instance but slightly) The other fun thing about playing with line weight is sometimes the lines don't have to connect!
Have fun with line weight! It's the best thing that could have happened to hand drawn art!