Weaboos, or Japanophiles as I'll call them, are almost inevitably linked to people who watch anime. It's a negative connotation that suggests the person lives in a fantasy world where anime is real (to a certain degree) and that living in another country will somehow solve all their problems.
So where does this all stem from?
Well, to begin with; the simplest answer is proximity. The majority of anime's target audience is Japanese people and therefore will have Japanese life reflected within it, which is why you don't see one of the kids on Coronation Street worrying about which Hummer to take to the prom. Therefore people who watch a moderate amount of anime will inevitably notice various Japanese quirks here and there. People who don't watch anime or other Japanese media probably won't see these anywhere else. Whether or not they choose to investigate further is down to personal preference.
The second point of being obsessed with Japan isn't without some truth. Take a look at the poll results in this article on working in Japan and this article on learning Japanese. 91% of readers would love to work in Japan, whereas 37% would like to learn Japanese. The trend that I'm noticing is "I would like to live in Japan" or "I'm going to live in Japan" but not "I do live in Japan". Let me put it this way: 99.4% of Japan is Japanese and of the 0.6% other, nearly half of that is Korean. Surely with the number of people claiming to going to move there that number, particularly of white British/Americans, would be significantly higher?
Why is this so?
Well, in my opinion, this is just simply something that everybody does, regardless of hobbies or lifestyIe The car enthusiast will believe that owning a Ferrari or Porsche would be the most awesome thing ever, the guitarist who thinks being able to play like Michael Angelo Batio would give him instant stardom, or even the virgin who wants to become a porn star. We all have that one dream that we wish to fulfill, but the problem with having a dream job/possession/whatever is that it is fragile: if it doesn't live up to expectations it can easily be shattered. So we then make up excuses to distance ourselves from accomplishing that dream (can't afford it, don't have the time, etc.) in order to maintain those wishes. We have wishes to give us goals and we have goals to give us direction in life.
I suppose what I'm trying to say is that the misconception that Japanophiles live in a fantasy is the same as any other person's dream or desire. The fact that it's directed at a country or it was instigated by anime doesn't make it any more or less worthy than anyone else's.
tl;dr - Don't be a ****, treat others dreams as you would treat your own.