"frankfurter," 1906, with slang sense of "penis" following soon after, from German wienerwurst "Vienna sausage" (see wiener). Meaning "ineffectual person" is 1963; pejorative sense via penis shape, or perhaps from weenie in the sense of "small" (see wee).
: You'd never know that weenie voice belonged to a gorilla
(also wiener or weener) A frankfurter; hot dog: this wienie and kraut combination(1911+)
(also wiener or weener) The penis; esp, the relaxed penis
(also weeniehead or weiner-head) An ineffectual, despised person; jerk, wimp: She plans to be a weenie, is a weenie, asks to be loved anyway, and is loved anyway/ Anybody who zips their coat when the temperature is higher than zero is an automatic weenie(1960s+)
(also ween) A very serious student; Greasy Grind, throat: Premeds known to their less pressurized campus colleagues as throats and weenies/ Weens are strange creatures with pallid faces, glassy eyes, and calculators strapped to their belts(1970s+ College students)