I've looked up Wikipedia's article on Hypocorism, which states (emphasis mine):
Hypocorisms include pet names or calling names, often a diminutive or augmentative form of a word or given name when used as a nickname or term of endearment.
The question Female Pet Names that a Londoner might use? on Writing.StackExchange lists names like "darling" or "sweetie" as examples of so-called pet names. I remember that I have heard the term used similarly before and Wikipedia lists these names in their article about term of endearment.
The article lists an example for French where "my duck" is apparently a pet name and I know that German has some examples that mean animals like "mouse" or "rabbit", but I couldn't find any evidence that this type of "pet names" are used in English, too, (except for the Wikpedia article on terms of endearment that lists "honey bunny" as one example throughout the text) or any indication that terms like these would be the origin of the phrase.
I was wondering what the origin of this phrase are: why are names like "sweetie", "cutie" and "honey" today often referred to as "pet names" in English?