Because this nickname is so common, this is the earliest occurrence of it:
Standin' right here, guns up boy
Weezy F, Birdman
More instances:      
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Blood game mothafucka, call me Red Alert
Young Carter kill in order, who get it first
It’s me, the rapper eater
Feed me, feed me, feed me!
Take them panties off, the pussy lookin' at me
I’m the pussy monster, now get the pussy ready
Hi, I’m the
Pussy monster, the pussy monster
The pussy monster, the pussy monster
Pussy monster in her closet, full of surprises
I give full body massages, I hope that pussy smell like a violet
Like Hitler, it’s the New Orleans Nightmare
Money so old it’s growing white hair
Hello world it’s Little Full Clip Me
Got-gotta wake yo ass up, can’t let the bullshit sleep
I go by Weezy, baby, so call me “Lil Weezle"
My city is New Orleans, baby, my street is Eagle
Goddamn, man, I am
L-I-L, Weezy, off the heezy
More instances:         
But you see I keep it pumpin', yeah I got that heart back
So just call me Lil Carter, or Lil Cardiac
Now just r-r-rock with Junior
I am the Little Big Kahuna, y'dig?