Marijuana might be the full meaning of MJ since it also have the "Em and Jay" in it. But the real MJ is from one of the history of Marijuana. There is this activist woman who fought well for legalization of Marijuana, well known as Brownie Mary.
Brownie Mary real name is Mary Jane Rathbun. The MJ we all calling today is from her name "Mary Jane". She became popular for her activism act of using marijuana to help cancer and AIDS patients in San Francisco. Aside from being a medical volunteer and cannabis activist, she's also a baker whom was said to be baking over 4000 cannabis infused brownies in a week.
She got arrested several time but her "Old Mama" looks made the media's sympathy for her. Her cases also woke up the media's and researchers to start doing something about marijuana. Although, it took sometime but she was later given permission in San Francisco to be doing her thing to keep helping those patients.
Marijuana can as well be the reason while MJ is call that, but Mary Jane took a strong part in this sphere which made the acronym to be more popular.