The difference between .5pt and 1.0pt is not visible on the screen due to the fact that 0.5 points equals only .006 inches. Monitor screen resolution is 96 dpi, so showing .006 of an inch on a 96 dpi screen is not possible.
Anything 1 point or less is shown as the same width, so that it does not disappear. When printed to a high resolution printer 600 dpi (or even 300 dpi), there is a difference in the outline width between 1 and 0.5. This can be tested in the Layout View by adding Polygon graphics and varying the outline width while zoomed in. This gives an idea of how the outlines will look when printed.