Origins
The word 'baby' is one of the most familiar words in the English language, yet its origins are surprisingly humble and uncertain. It appears in Middle English around 1377 as 'babi,' likely formed as a diminutive of the slightly older word 'babe' (attested from about 1230) with the addition of the affectionate suffix '-y' or '-ie.' The underlying source is almost certainly imitative — an attempt to render in language the babbling sounds that infants themselves produce.
The consonant /b/ is among the very first speech sounds that human babies make, because it requires only the simplest articulatory gesture: closing and opening the lips while voicing. This is why 'mama,' 'papa,' 'baba,' and 'dada' appear as nursery words in languages all over the world, from Mandarin to Swahili, without any need for a common ancestor. The English words 'babe' and 'baby' belong to this universal pattern, and linguists generally classify them as onomatopoeic or 'nursery formations' rather than tracing them to a specific Proto-Germanic or Proto-Indo-European root.
The word 'babe' appeared first, recorded in the early thirteenth century. 'Baby' followed in the late fourteenth century and gradually displaced 'babe' as the standard term for an infant. By the sixteenth century, 'baby' had also acquired figurative senses: a term of endearment for a loved one, and a metaphor for anything small or immature. Shakespeare used both 'babe' and 'baby' freely in both literal and figurative senses.
Development
English 'baby' was so successful that it was borrowed into dozens of other languages. French 'bébé' entered the language in the early nineteenth century, borrowed from English. From French it passed into Spanish as 'bebé,' Portuguese as 'bebê,' and Italian as 'bebè.' German borrowed 'Baby' directly from English in the twentieth century, and it is now standard colloquial German. Japanese borrowed it as 'ベビー' (bebī). The global spread of the English word has made 'baby' one of the most internationally recognized words of English origin.
The related word 'babysit' is a surprisingly recent back-formation, first attested only in 1947, derived from the agent noun 'babysitter' (1937). The word 'babble,' meaning to talk incoherently, also derives from the same imitative base, recorded from the thirteenth century. 'Baboon,' despite a superficial resemblance, has a different origin — it comes from Old French 'babouin,' probably from 'baboue' (grimace).
The diminutive formation pattern seen in 'baby' (base word + '-y') is extremely productive in English nursery language: 'doggy,' 'kitty,' 'daddy,' 'mommy,' 'tummy.' This suffix carries connotations of smallness, affection, and intimacy, and its attachment to 'babe' transformed a plain monosyllable into one of the most emotionally charged words in the language.