1540s, imbecille "weak, feeble" (especially in reference to the body), from Middle French imbecile "weak, feeble" (15c.), from Latin imbecillus "weak, feeble," a word of uncertain origin.
The Latin word traditionally is said to mean "unsupported" or "without a walking stick" (Juvenal: imbecillis: quasi sine baculo), from assimilated form of in- "not, opposite of" + baculum "a stick" (see bacillus), but Century Dictionary finds that "improbable" and de Vaan finds it "very far-fetched" and adds "it seems to me that exactly the persons who can walk without a support are the stronger ones." There also are phonological objections.
Sense shifted to "mentally weak or incapable" from mid-18c. (compare frail, which in provincial English also could mean "mentally weak"). As a noun, "feeble-minded person," it is attested from 1802. Traditionally an adult with a mental age of roughly 6 to 9 (above an idiot but beneath a moron).