Weeabo is intended to be a derogatory insult, along with Wapanese. Incidentally, "Otaku" is considered an insult in Japan. They think it's weird that foreign fans are proud to call themselves as such.
A nicer way to think of it is that anyone who calls you a Weeabo is xenophobic as hell & resents you for not thinking their preferred culture is superior in every way.
It's primarily aimed at shameless obsessive otaku, especially the noobs who have only been into anime for about 5 years. But much like how Hipster has lost all meaning & has no definitive definition, it's also used by anime haters to describe anyone who likes anime.
Also used within the fandom, aimed at passionate noobs, used by older fans who've long settled into the fandom like a marriage where you stay because it's familiar, but the romance is gone. The noobs remind them of how embarrassing they themselves once were.
Anyway, Weeabo characteristics are the following:
*Bringing anime & manga into any conversation it has no business being.
*Wearing cosplay outside of a convention.
*Proudly displaying your poorly drawn shipping fanart on the internet.
*Being able to name all the Pokemons AND not hating the Final Fantasy franchise.
*Constantly reminding people that English music sucks & American musicians are unattractive (still guilty as shit of this on my part).
*Being a proud & open fan of yuri, yaoi, shotacon, lolicon, sibling complex, or furries. (Guilty of some of this too, but America needs to get over it's damn homophobia already).
*Using Japanese words in conversations with non anime fans. (Incidently, this also irritates the shit out of seasoned anime veterans).
*Getting extremely defensive when another otaku points out that your're mispronouncing a word or using it incorrectly.
*Having a ship-to-ship combat in public.
Getting toxic when more well-behaved otaku tell you that your embarrassing yourself as well as them.
*Owning an obscene amount of UFO cather dolls & NECA figurines.
*Owning a mouse pad with a boob armrest & a body pillow with a naked anime character on it.
*Having hentai, wallscrolls, & manga posters on your walls instead of pinups of real people.
*If being a fan of anime is literally your only defining characteristic at school, then Weeabo is actually a well-deserved title used to label a one-character.
From what I've heard, a weeaboo is a person that says they know everything about anime/is an anime fan, but actually doesn't. You probably aren't a weeaboo, though. If you don't want to seem like one, refrain from over using words like "kawaii" "desu", etc.
Basically it means someone who likes anime A LOT to the point where they put Japan on a high pedestal and think it's the best place on earth and it's only anime and they generally put down America/other countries to make Japan look better and they force anime onto other people and can't understand why a person doesn't love it. It's really not a nice thing to call someone, and there's a lot of negative traits associated with it including forcing (usually yaoi) parings on people, harassing Asians (because they think they're all Japanese) really bad cosplay in inappropriate places, speaking in broken Japanese pretending to know the language (desu, sugoi, kawaii,and neko are usually some favorites), and drawing bad fanart/fanfictions and forcing people to look at it thinking they're the best and that they have no need for improvement, the list goes on, if you want here's a funny tumblr all about people's encounters with them.
When you're friend said you're a weeaboo for Len they probably meant that you're super obsessed, think he's the best singer ever etc. Now I don't know you or them or how they said it so they may have just been joking, but Weeaboo is usually meant as an insult.