Someone who obsesses over Japanese media, and to a lesser extent, culture. Like, fetishizes it.
Usually insufferably so - I might only use it as an insult or a self deprecating term.
Japan makes a lot of cool stuff, but enjoying things specifically because they come from Japan is what makes you a weeb, in my eyes.
I love animation, and watch a lot of it. I don't view Anime as a separate entity from other animation, not really; I don't watch anime for the sake of watching anime, if that makes sense. That's something I might (sometimes lovingly, other times not) describe as a weaboo doing in my head.
It's harmless though, as long as you're not toxic about it. I would never actually use "Weeb" aloud in conversation or even written out directed at someone as a jab, as it's just a hobby or interest, and I can't reasonably get upset at that. But like "nerd", I find it easy to dunk on the collective "weeb culture" when it shows it's many pockets of toxicity.