Green’s Dictionary of Slang

(US) a tall and/or thin person, thus as nickname.

1895		Mirror of Life 7 Dec. 14/3: Stapleton [...] was like a beanstalk, and, for his weight, had reached the extraordinary height of 5ft 9½in.
1896		Leeds Mercury 8 Feb. 12/3: ‘Egad, I never knew such luck as thine, old Beanstalk’.
1953		F. Paley Rumble on the Docks (1955) 75: His eyes moved to Wimpy. ‘How about the beanstalk?’.
1967		Coventry Standard 18 May 8/4: Are you what the little people would call a beanstalk or a lofty?
1971		T.C. Bambara ‘Raymond’s Run’ in Gorilla, My Love (1972) 29: He’s got no right to call me Squeaky, if I can’t call him Beanstalk.
[1981		Belfast Teleg. 16 Sept. 12/5: [headline] Frank’s thin as a beanstalk].