Learn English – Was “precious snowflake” originally used in a derogatory manner

According to the Oxford English Dictionary, the word baby is formed from babe + the -y suffix. Further, they add that baby is likely from baby-talk:

The English word was borrowed into many other European languages; compare e.g. French baby (1704 in sense ‘small child’, 1793 as a term of endearment, 1898 in sense ‘doll’), Italian baby (1877), Dutch baby (1875), German Baby (second half of the 19th cent.), Danish baby (late 19th cent.). C

Compare also French bébé (c1755 as a term of endearment, 1858 in sense ‘small child’, 1885 in sense ‘doll’), which has often been considered a loan < English, but perhaps (in spite of its late attestation) shows a parallel formation < the (reduplicated) syllable /be/ , characteristic of early infantile vocalization.

Baby is attested to circa 1400, while babe is noted from the late 1300s. Note also that babe, though the origins are unknown, is likely to have formed from baby-talk as well:

Origin uncertain. Probably either < a (reduplicated) syllable /ba/ which is characteristic of early infantile vocalization (and which probably also directly or indirectly underlies baba n.7, baba n.2, baba n.5, baba n.6, babble v.1, etc.), or perhaps shortened < baban n. (which is only attested in a few texts, although its scanty attestation may be due to the fact that it belongs to an informal register, and so would have been more frequent in spoken than in written usage; with the shortening process involved, compare e.g. Gib gib n.1, Tom Tom n.1, Will Will n.3, and similar pet forms of forenames).

Both words emerged around the same time (in written usage, at least), and may both be from forms of baby-talk. If babe is from early infantile vocalization, as is noted, it is possible that baby is not actually a hypocoristic form because they are both from baby-talk. However, if babe is a shortening (the other possibility), then baby would be a hypocorism.

Since it's slang, it's going to be hard to pin down the exact origin of the phrase. I can think of two plausible derivations:

1. The skin of a bruised eye is going to be swollen and pulled taut, and thus more reflective and "shiny" than the surrounding skin. I think this is secondary.

2. The most plausible metaphor: Shoe shiners are not as common now as they were in the early 20th century. "Shiner" could refer to how the unfortunate person hasn't gotten their shoe shined, (usually with black shoe polish,) but rather the eye.