Unfortunately the stereotype (and all stereotypes, really) stuck because some people took things to the extreme. Somehow, in the more underground/less mainstream culture, the vogue was to emulate it, but not in a traditional "healthy" manner. I know though that while the internet boosted the rate at which folks who would eventually contribute to the label's current definition sprung into existence, it was still already around. Such folks hung out at those unknown importer shops in Asian "towns" in cities - there just weren't as many before the intertoob media sharing age.
I have trouble with labeling people weeaboos mainly because ignorance is not always easy to gauge in my opinion. You can be ignorant because you simply know no better or you can choose to be ignorant. Personally, it's that distinction that counts more. Those that are engrossed in a subset culture and somehow mentally extrapolate it to be a general representation of the whole culture kinda do fall in that generally defined label, but is that really the problem? I think just based off this entire thread so far, we've come to the consensus that it's ignorance, and generally that's not very defensible. We do live in the internet age, so save for actual cultural immersion, it's not hard to do some research any gain a bit of understanding on a topic. One of the major counterpoints to this though would be that we've also seemingly degenerated in several aspects of social interaction - whether or not that has significantly contributed to the weeaboo subculture can be debated.