Why
I don't think either answer so far is right, I personally think there must have been the nickname before the song, and for the person whom said he smoked lots of pot, I know what a shotgun is however shotguns are something high school kids do, I can't see Willie Nelson giving people shotguns, willie seems like the type of dude who would roll you your own j and him his own j.

Well, the song helps, but he is notorious for smoking "pot" and there is a type of "toking" known as "shotgun"!!

(not that I know anything about that kind of stuff)
lol

He sang a song named "Shotgun Willie" the name just kind of stuck after that.