I would guess it derives from the folksy way of calling the state Virginny, as in "take me home to old Virginny," or, "carry me back to old Virginny." Hence the tobacco crop there is called "'ginny weed."
I only know Virginny in the context of the song lyric. Never heard of Ginny Weed per se either. It could be from Virginia tobacco farmers or from blenders, but I'd never heard it. Or it might just be a coinage from one person. Dunno.