I'd read about this on GoNintendo a while back, actually.
Supposedly the WeeMees were around before the Wii (EDIT: I mean, around before the idea of Wii Miis were revealed)...obviously the WeeMees got a lot more attention after Nintendo revealed their Wii Miis. I think it's a coincidence.
It's not like Nintendo ripped off the idea of purple GameCubes from the TV show ReBoot. (Which, as I pointed out (and edited into the ReBoot Wikipedia article), the first of the final two TV movies that ended the series was shown on YTV in Canada on the very same day the Nintendo GameCube launched in North America. (Kind of funny when Dot says "Where's a Game Cube when you need one?" on that very day.)
And even if Nintendo did rip off WeeMees, it's not like the WeeMee people will be able to do much about it, probably.
(I miss ReBoot and hate how it ended on a cliffhanger before the writers disbanded and that Mainframe makes shows that I wouldn't watch now like Barbie movies and others based on toylines I don't care about. Beast Wars (or Beasties in Canada) and Beast Machines (to a certain extent) were cool though. Even the odd Action Man episode was amusing, but now...ick.)