Otaku is more than just being someone who loves manga/anime too much. It's more like being a recluse that'll focus so much on their interest (manga/anime, idols, games, trains, anything you can think of) that they'll forgo any other things (like spending time with "normies" or sometimes even working) in order to spend more time with what they like. Considering the extreme fanaticism of some people over there regarding certain things (like idols or seiyuu, going to the point of stalking or trying to attack the object of their admiration), I guess that it can be a bit of a mental illness. (Example: 3DPD)
A weaboo, on the other hand, is someone whose Japanophilia is on otaku levels of extremity. Like girls who abuse the words kawaii, baka, desu, etc., because of their fanaticism, or dudes who claim waifus and all that because JAPAN IS SO MUCH BETTER THAN AMERICA BAKA GAIJIN blah blah blah. It later becomes the standard reason why some people are afraid of admitting they like it.
Neither are healthy ways to live or act. Later ostracism and bullying can and will happen, because anything that's different isn't welcome. Granted, we should be in a time where people just accept likes and dislikes normally, but let's be honest: Human nature leads to us wanting to feel superior to others and name-calling and bullying to feed our egos.
Just my $0.02