Classic definition of a weeaboo is someone who is completely obssessed with anime and Japan in general, to the point of wishing that they'd been born Japanese or dreaming of moving to Japan one day and marrying a qt 3.14 nihonjin. Typically they will show an ironic level of misinformation towards the subject matter they devote so much of their free time to since all of their "research" is conducted by watching random anime. Despite this they will consider themseves to be experts on all things Japanese despite having never ever been to the country.
Basically, you can like anime and be interested in Japan without being labeled a weeb as long as you don't go completely overboard. Kinda like any other hobby or interest, really.
