Origin and history of their

possessive pronoun, "their own, their people, land, etc.," early 14c., from their + possessive -s, on analogy of his, hers, etc., but in form a double possessive. The same pattern happens in the earlier pronoun, native hiera, here "their;" attested by late Old English as heres.

nominative case pronoun of the third person plural, "persons or things in question or last mentioned," c. 1200, from a Scandinavian source (Old Norse þeir, Old Danish þer, þair), originally a masculine plural demonstrative pronoun. By c. 1400 it had displaced Middle English he, hei, from Old English hi, hie, plurals of he, heo "she," hit "it."

The most important importation of this kind [from Scandinavian to English] was that of the pronomial forms they, them and their, which entered readily into the system of English pronouns beginning with the same sound (the, that, this) and were felt to be more distinct than the old native forms which they supplanted. Indeed these were liable to constant confusion with some forms of the singular number (he, him, her) after the vowels has become obscured, so that he and hie, him and heom, her (hire) and heora could no longer be kept easily apart. [Jespersen, "Growth and Structure of the English Language"]

The Scandinavian source of they is from Proto-Germanic *thai, nominative plural pronoun, from PIE *to-, demonstrative pronoun (see that).

From c. 1400 as "people in general." Colloquial use of they for "anonymous people in authority" is attested from 1886. They say for "it is said" is in Milton.

With reference to singular nouns by 1520s, especially with words in every, any, etc.

[Y]ou desire to be just and honest and to give every Body their due .... [William Notcott, "Jesus Christ Most Precious to Every True Believer," 1735]

emphatic plural pronoun, c. 1300, from their + self, with self, originally an inflected adjective but here it has come to be treated as a noun meaning "person." Related: Theirselves. Compare themselves.