Of course you can change the thickness of the line.
You need to use a java.awt.Graphics2D object (the Graphics object passed to paintComponent() is actually Graphics2D, so you can simply cast it), then use a java.awt.BasicStroke object for drawing.
Find the 2D part of the Java tutorial, and go forward until you get to the bit about "stroking and filling." That shows how to draw a rounded rectangle with a dashed stroke; you can use the same technique for different thicknesses.
Minor spelling error. Also I forgot to say you can find "stroke and fill" under "working with geometry" on the link I gave you.[/edit] [ October 12, 2007: Message edited by: Campbell Ritchie ]