Besides hacking code, or possibly a plugin, I don't know of any way to add stroke presets to drop down.
You may define hairline differently, but here is how I look at it. Hairline is the finest line that can be reproduced for intended media. For the web and screen display, one pixel is the finest line, and with pixels as the stroke weight unit, 1 px would be a hairline. For print, .25 pt is typically what is considered a hairline. If you change the stroke unit to points, .25 pt will be the first weight in the drop down.
Somewhere along the way I must've accidentally changed it to pixels. Thanks!
As far as ID is concerned, points and pixels are the same size...
That works in print, but you can't, as jeffrey points out, light up less than one pixel on screen.