Being weeb means you adore Japan, which isn't the case for most of us, I believe, but disregarding that, the most significant anime for me might have been Elfen Lied. It's no masterpiece, it's barely decent objectively speaking, but back then I hadn't watched much anime at all, and it really made me think: "Holy shit, there are TV series like this around!" Would I recommend it to people? Nah, I don't think so. But it was totally different compared to all the Western stuff I'd mainly watched so far in my life, so I ended up really delving into anime after it.