Why does English employ double possessive pronouns such as theirs and ours?

I am a native speaker of AmE. I understand when and where to use their vs theirs, etc. etc. (i.e. Don't migrate this to ELL!). I've searched the site and google, and I have not quite seen an answer to my question.

Etymonline describes the word theirs as:

possessive pronoun, "their own," early 14c., from their + possessive -s, on analogy of his, etc. In form, a double possessive.

And, their:

plural possessive pronoun, c. 1200, from Old Norse þierra "of them," genitive of plural personal and demonstrative pronoun þeir "they" (see they). Replaced Old English hiera. As an adjective from late 14c. Use with singular objects, scorned by grammarians, is attested from c. 1300, and OED quotes this in Fielding, Goldsmith, Sydney Smith, and Thackeray. Theirs (c. 1300) is a double possessive. Alternative form theirn (1836) is attested in Midlands and southern dialect in U.K. and the Ozarks region of the U.S. Emphasis mine

(Parenthetical question, what do they mean by use with singular objects in this case?)

The entires for our and ours are similar.

Why does English have a double possessive pronoun? And why does modifying it thusly change its usage? Singular-plural possessive pronoun - possessive adjective; double-plural possessive pronoun - possessive pronoun?

Theirs is used when there is not a following noun, but, I don't understand why a double possessive would be used in this way.

The book is theirs.

That is their book.

We cannot say:

The book is their.

nor

That is theirs book.

But, for the life of me, I cannot figure out why making it a double possessive would make this happen!

Answer

I don't know why etymonline calls theirs 'a double possessive', but it's not.

The unfortunate terminology of 'the double possessive', aka 'the double genitive', is not due to the pronoun theirs itself but to the common construction like a friend of theirs where traditional grammar treats the preposition of as another possessive on top of the possessive pronoun theirs.

So in a construction that doesn't contain of, theirs itself is no double possessive:

The book is theirs.

This example of yours, for example, doesn't contain of, so there's only one possessive, the possessive pronoun theirs, which means their book. (Note the subject of the first clause does contain of, so you can call it a double possessive.)

Now, some grammarians don't like the term 'the double possessive/genitive' even for constructions like a friend of theirs.

The Cambridge Grammar of the English Language (Page 468), for example, treats She's a friend of Kim's not as a double possessive/genitive but as a oblique genitive:

...we do not regard of as a genitive case marker, and hence there is only one genitive here, not two.

As for the distinction between their and theirs, CGEL classifies the former as a dependent genitive (possessive) and the latter as an independent genitive (possessive), which easily explains why these don't work:

*The book is their.

*That is theirs book.