1540s, imbecille "weak, feeble" (especially in reference to the body), from 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).
early 15c., imbecilite, "physical weakness, feebleness (of a body part), impotence," from Old French imbécillité and directly from Latin imbecillitatem (nominative imbecillitas) "weakness, feebleness, helplessness," from imbecillus "weak, feeble," of uncertain origin (see imbecile). "Weakness in mind" (as opposed to body) was a secondary sense in Latin but was not attested in English until 1620s.
late 14c., "imbecile, one who is in dotage or second childhood;" see dote (v.) + -ard. Sense of "one who dotes, one who is foolishly fond" (c. 1600) is now rare or obsolete. Other noun derivatives of dote, all in the sense "fool, simpleton" in Middle English were dotel (late 14c.), doterel (late 15c.), doti-poll (c. 1400; see doddypoll).