Does the word "obsessed" always have a negative meaning? No. It is a matter of degree. You can be obsessed with something meaning that you really love it, that you are really into it. That is a positive. I am obsessed with learning Korean. = I am really interested in learning Korean. I am obsessed with watermelons. = I really love watermelons. However, if you are obsessed with negative things OR if your obsession takes over your life, then it is a negative. I am obsessed with knowing every single detail of my friend's personal life. I am so obsessed with learning Korean that I only get one hour of sleep every night.

http://www.thefreedictionary.com/obsessed "To have the mind excessively preoccupied with a single emotion or topic" "Excessively" means "too much" and generally has a negative connotation. What Mojave said might be true but that's a discussion on psychology and not grammar.