Basically it means someone who likes 아니메 A LOT to the point where they put 일본 on a high pedestal and think it's the best place on earth and it's only 아니메 and they generally put down America/other countries to make 일본 look better and they force 아니메 onto other people and can't understand why a person doesn't 사랑 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 당신 want here's a funny tumblr all about people's encounters with them.
link 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 당신 또는 them 또는 how they said it so they may have just been joking, but Weeaboo is usually meant as an insult.