Basically it means someone who likes アニメ A LOT to the point where they put 日本 on a high pedestal and think it's the best place on earth and it's only アニメ and they generally put down America/other countries to make 日本 look better and they force アニメ onto other people and can't understand why a person doesn't 愛 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 一覧 goes on, if あなた want here's a funny tumblr all about people's encounters with them.
link When you're friend 発言しました 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 あなた または them または how they 発言しました it so they may have just been joking, but Weeaboo is usually meant as an insult.