late 14c., babi, "infant of either sex," diminutive of babe (see babe) with -y (3). Meaning "childish adult person" is from c. 1600. Meaning "youngest of a group" is by 1897. As a term of endearment for one's lover it is attested perhaps as early as 1839, certainly by 1901 (OED writes, "the degree of slanginess in the nineteenth-century examples is not easily determinable"); its popularity perhaps boosted by baby vamp "a popular girl" (see vamp (n.2)), student slang from c. 1922.
Meaning "minute reflection of oneself seen in another's eyes" is from 1590s (compare pupil (n.2)). As an adjective by 1750. Baby food is from 1833. Baby blues for "blue eyes" recorded by 1892 (the phrase also was used for "postpartum depression" 1950s-60s). To empty the baby out with the bath (water) is attested by 1909 (in G.B. Shaw; compare German das Kind mit dem Bade ausschütten, attested from 17c.). A baby's breath was noted for sweet smell, which also was supposed to attract cats, hence baby's breath as the name of a type of flower, attested from 1897. French bébé (19c.) is said to be from English, but there were similar words in the same sense in French dialects.
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. [Hensleigh Wedgwood, "A Dictionary of English Etymology," 1859]
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Now mostly superseded by its diminutive form baby.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.