late 14c., "infant, young child of either sex," short for baban (early 13c.), which probably is imitative of baby talk (see babble (v.)). In many languages the word means "old woman" (compare Russian babushka "grandmother," from baba "peasant woman"), and it is also sometimes a child's variant of papa "father."
The simplest articulations, and those which are readiest caught by the infant mouth, are the syllables formed by the vowel a with the primary consonants of the labial and dental classes, especially the former ; ma, ba, pa, na, da, ta. Out of these, therefore, is very generally formed the limited vocabulary required at the earliest period of infant life comprising the names for father, mother, infant, breast, food. [Wedgwood]
Crist crid in cradil, "moder, baba!" [John Audelay, c. 1426]
Now mostly superseded by its diminutive form baby. Used figuratively for "a childish person" from 1520s. Meaning "attractive young woman" is 1915, college slang (baby as "girl, young woman, girlfriend" is attested by 1839; see babe). Babe in arms is one so young it has to be carried; babe in the woods "an innocent among perils" is from 1795.