Jen Doll offers a history of terms of endearment:
Babe and baby as used to describe a romantic partner (rather than a small child or immature person; those usages began in the 1400s and 1500s) can be traced to usage that began in the 19th and 20th centuries in America. Initially, the words were simply used as a form of address (men were calling each other baby in 1835, sans any romantic connotations; in the 1996 movie Swingers, Vince Vaughn’s character employs the word for just about everybody).
The Oxford English Dictionary gives the first romantic use of babe as 1911, exampled by the Rodgers and Hart lyrics, “Oh, ma babe, waltz with me, kid. Gee, you’ve got me off ma lid.” In 1684, there’s an isolated use of baby by Aphra Behn: “Philander, who is not able to support the thought that any thing should afflict his lovely Baby, takes care from hour to hour to satisfie her tender doubting heart,” but the word doesn’t pop up again as a romantic descriptor until the 1860s: “Dear, dear, dear Baby, how often, how incessantly I think of you,” writes General H. M. Naglee. Baby is also used around that time to refer to “attractive young women,” and babe follows in that role in 1915, though it takes until 1973 for babe to apply to a man: “He’s a real babe … Mr. America!”
Before those two little b-words, though, came handfuls of nicknames you might apply to your lover, including cinnamon (1405), honeysop (about 1513), heartikin (1530), ding-ding (1564), pug (1580), sweetikin (1596), duck (1600), sucket (1605), flitter-mouse (1612), nug (1699), treat (1825), hon (1906), sugar (1930), and lamb-chop (1962). According to Katherine Connor Martin, head of U.S. dictionaries at Oxford University Press, “Really common endearments involved sweetness, sugar, and animals and birds. This baby concept is not something that has a long history. We can thank American English for innovating this particular strand.