No it doesn't.
"Weeaboo" is an offensive, derogatory term to describe a non-Japanese native being overly obsessed with its culture; cosplaying, collecting memorabilia, fornicating with a body pillows, etc... The term is deemed very offensive as it's often used in a very negative connotation.
We all enjoyed cartoons as children, anime is no different to that. All the arguments claiming enjoying anime makes you this or that is simply speculation, it's highly dependable on the kind of anime you watch.
It's no different to other media out there or western cartoons, for that matter...
Have a good day.
EDIT: General corrections and more text added.