Proper meaning of the slang "Baby"

Question

• Let him do it because it's his baby.

• Don't push this job on me because it's your baby, not mine.

• This classic show car is his baby.

• Hey baby, how are you doing today?

I understand that the speaker used the word baby to describe work in the first and second examples. The 3rd example is confusing me. How can a car be one's work? Please help improve my understanding.

I know the slang word baby means "a woman who is young", as in the last example, someone is talking to a woman/girl.

Answer 1

You've slightly misinterpreted the word baby in your first three examples. It means something in which one has invested time, interest, and emotion and for which one has a proprietary feeling. Speaking hyperbolically, it's as though the object of interest is like one's own child.

I thought I should add an example of the usage that didn't involve work- or job-related situations. This turned out not to be as easy as I thought. There's even a canonical political cartoon, showing Hoover turning over the problems of the Depression to Roosevelt in 1933, captioned "It's his 'baby' now":

But I finally found a story about a man who as a hobby, salvaged his car that had been in an accident, replacing the metal body with one made entirely of wood. From that story:

So, he started salvage [sic] spruce wood from construction sites, adding up bit-by-bit to his truck every evening after work for about nine months. So you can say it’s his baby now.

A labor of love, with a play on the nine-month "gestation" period for the "baby."

Answer 2

Baby in the first three sentences means:

• Slang An object of personal concern or interest:

while in the last one it refers to:

• Sweetheart; dear. Used as a term of endearment.

(AHD)

The term baby: (Etymonline)

• dates back to the late 14c., babi a diminutive of baban.

• As a term of endearment for one's lover it is attested perhaps as early as 1839, certainly by 1901; its popularity perhaps boosted by baby vamp "a popular girl," student slang from c. 1922.

• From which, probably, its slang usage to refer to an object of concern or interest.