Thee, thou, and thine (or thy) are Early Modern English second person singular pronouns. Thou is the subject form (nominative), thee is the object form, and thy/thine is the possessive form.
Before they all merged into the catch-all form you, English second person pronouns distinguished between nominative and objective, as well as between singular and plural (or formal):
thou - singular informal, subject (Thou art here. = You are here.)
thee - singular informal, object (He gave it to thee.)
ye - plural or formal, subject
you - plural or formal, object
Interestingly, when the first English translations of the Bible were being made, the informal thee and thou were used specifically in reference to God to indicate an approachable, familiar God, but as the language changed this paradoxically brought thee and thou to sound more formal to the modern English speaker.
I think this may be a variation on the BrE expression "for two pins", which means:
At the slightest provocation; for the smallest reason.
Farlex Dictionary of Idioms (via TFD)
I assume that "pins" here refers to the type used in sewing or another practically worthless type of pin.
The earliest attestation of this idiom that I found so far is from 1890:
For two pins I'd put a match in every gunyah on the place.
The Squatter's Dream: A Story of Australian Life
Here's another early example from The Times (London, 1794):
I'll blow you up for a sodomite, for two pins.
There are other, older idioms where pins are worthless (note that the expression most likely refers to pins made of wood or bone, not metal). "Not worth a pin", "wouldn't care a pin", etc.:
He seide al þat he had ywonne
Jn þe werlde vnder sonne,
He nolde ȝiue þere-of a pynne,
Bot he miȝth þise wynne.
He said all that he had won
In the world under the sun,
He wouldn't give thereof a pin,
If he might win this.
Kyng Alisaunder
See 9. b for more quotes (and a definition) from Middle English.
It was even used by Shakespeare:
A round hose, madam, now's not worth a pin.
The Two Gentlemen of Verona
It's worth mentioning that I found the exact same expression "for a couple o' pins" in:
- The Leisure Hour (1904):
[F]or a couple o' pins I'd shteam-rowl yez under the two feet o' me.
- The chimney corner (1879):
See now, for a couple o' pins I'd take both yerself an' the little sweep ye call 'John' to the lock-ups!
Best Answer
In "I thou thee", "thou" is a verb. The relevant definition in the OED is:
(The quote in your question is one of the examples listed for this sense, in fact.)
It's really the same pattern as "Don't 'honey' me!" which you may have actually heard in real life.
To understand the reason this was an insult, one must be aware that "thou" at this time was a familiar pronoun of the second person singular while "you", the plural, had come to be used in the singular for people owed a certain measure of respect. (Compare French "tu" and "vous", if you're familiar with French.) Therefore, to "thou" someone whose relationship to the speaker would ordinarily call for the use of "you" was a show of grave disrespect.