If all weapons do 1d6 damage, shouldn't I be a cheapskate and just buy daggers?
No. Don't be stupid. If you are swinging a dagger and the other guy has like a claymore you are in bad shape. We represent this by giving you a -2 penalty to your AP, because you just don't get as many opportunities to slip past his guard when his guard is like the length of your entire body. Get your self a grown-up weapon!
On the other hand, if you're bold enough to leap past that six feet of pointy death and like wrap your legs around the guy and just keep stabbing at him until he stops twitching, the advantage is yours, because it's really hard to use a claymore or a spear or something to scrape a crazy bastard off your chest. So that's useful.
Also, different weapons are good for different things. Like, chopping and stabbing isn't the best way to go against things that are already dead. They don't really bleed and the meat you cut off is probably just slowing them down. For those guys, you want to whack 'em with something blunt, like a mace, until the bones are powder. Stuff like that.