"Hear hear" or "here here"

It's "Hear! Hear!" which comes from "Hear him! Hear him!"

"Hear him! Hear him!"

"Hear him! Hear him!" was referred to in Debates in Parliament in 1688, and from the context it's clear it was a commonly heard phrase at the time.

Sir Edward Seymour.] I see Gentlemen speak here under great disadvantages. If they are not free in this Convention, what shall we do in Parliament ? When Gentlemen speak with Reflections, and cry, " Hear him, hear him," they cannot speak with freedom. I speak not this to the Chair (the Speaker) who keeps Order well, but to what passed at the Committee.

Seymour continues, and is followed by:

Sir Henry Capel.] The Chair has taken care of Order' and I have seen no disorder to-day. When Seymour was in the Chair, I have heard "Hear him, hear him," often said in the House.

"Hear! Hear!"

A interesting non-parliamentary use of "hear, hear" can be found in a 1770 A Letter to Lord Mansfield. A North Briton Extraordinary:

Note the parenthetic interjections to the quoted text:

(do you hear my Lord?) ... (hear, hear!) ... (do, for God's sake, my Lord, hear, recall your wandering thoughts, this is only a history) ... (once more hear, and I have done)

Originally from 1772 is what looks to be a satire on parliament in The Batchelor: or Speculations of Jeoffry Wagstaffe, Esq, Volume 3 that shows a transitional "hear, hear him":

Omnes.] Hear, hear him ; well spoke, no governor, no minister, no administration : long life to Will Spitfire, Doctor Bolus, Lord Babeltongue, and Dir Ed-w-d N-n-m.

Finally, in 1777 is an actual transcription of "Hear! Hear!" in The Parliamentary register: or, History of the Proceedings and Debates of the House of Commons:

The Governor took notice of the scandalous means made use of to vilify Lord Pigot, and depreciate his character through the channel of the news-papers. [Here a loud cry of Hear! Hear!] In particular, respecting the article of presents. It is true, his Lordship did receive a few trifling presents ; he wished he had not. They consisted of a cow, an elephant, two mares, and a gold tea service, to the amount of 500l. which he presented to his daughter, then lately married.

It's "hear, hear". Both Wikipedia and phrases.org.uk cite its origin as the UK Parliament. From the former:

It was originally an imperative for directing attention to speakers, and has since been used, according to the Oxford English Dictionary, as "the regular form of cheering in the House of Commons", with many purposes depending on the intonation of its user. Its use in Parliament is linked to the fact that applause is normally (though not always) forbidden in the chambers of the House of Commons and House of Lords.

The phrase "hear him, hear him!" was used in Parliament since the late 17th century, and had been reduced to "hear!" or "hear, hear!" by the late 18th century. The verb hear had earlier been used in the King James Bible as a command for others to listen.

The phrase is properly "Hear, hear", since you want everyone to hear what's being said.

Nonetheless, the eggcorn "Here, here" is so common that it may actually be eclipsing the original version.

I think we can dismiss the biblical claims to origin.

If we want to be specific to the phrase, then we can't find either "hear, hear" or "hear him, hear him", in any of the early bible translations, though we can certainly find hear in the imperative, it is not the same phrase. It also requests that you listen to the speech it itself is reporting, rather than to another person who is currently speaking.

If we're going to allow a bare hear, used to prefix one's own speech or report of speech to count, then we might as well allow Hwæt!, the first word in Beowulf to count, giving it a date of between the 8th and 11th century, depending on who you believe on that matter.

As an expression, we're left with late 17th Century use in the British Houses of Parliament.