Origin of "I'm gonna tan your hide"

If I were to take this literally, I might think this meant that someone was going to strip me naked and tie me to to a palm tree on a sunny day. I also understand that tanning refers to the process by which leather is cured, whether by chemicals or UV exposure. Growing up in the states, I know this to mean that you're about to get a thorough ass whooping.

It seems obvious that this idiom take it's origins from the way that leather is processed, but what is the relationship? Are hides physically beaten as part of the tanning process? Is it hyperbole that you're going to skin someone and make a nice purse out of them? Or maybe the nice red color your butt takes on after a good lashing?

The reference is to the tanning process in leather making (as you've guessed) and The American Heritage Dictionary of Idioms, Second Edition (by Christine Ammer) provides more details:

This term uses hide in the sense of "skin". The allusion in the first expression is to a spanking that will change one's skin just as chemicals tan animal hide (convert it into leather). [Second half of 1600s]

In ancient times, in the tanning process, the skin might have been beaten to remove the flesh and fat; however it is not the only method mentioned as some sources say that sharp stones or bones were used for scraping the skin as well. In the seventeenth century (the era when the idiom is originated), the tanning process didn't involve beating in the defleshing step. The skin is stretched and scraped with defleshing tools. Beating is mentioned in some sources as a method of softening the skin but it is usually done after the tanning process. (Here is an article about tanning in the seventeeth century: https://www.nps.gov/jame/learn/historyculture/tanning-in-the-seventeenth-century.htm)

Further supporting evidence from the book The Dictionary of Clichés: A Word Lover's Guide to 4,000 Overused Phrases and Almost-Pleasing Platitudes by Christine Ammer again:

tan someone's hide, to To give someone a beating. This term, in which the human skin is referred to as a hide (as it was from about the seventeenth century), may be on its way out, viewed with the same disfavor now accorded to _{SPARE THE ROD}. Nevertheless, during the years when corporal punishment was considered a normal procedure, it became a cliché. (Incidentally, the tanning process, in which animal hide is converted into leather, does not involve beating but rather a soaking in chemicals.) The expression dates from the seventeenth century. Charles Coffey used it in The Devil to Pay (1731): "Come and spin . . . or I'll tan your hide for you."

In OED, the earliest example is from c1670:

Expost. Let. Men Buckhm. 2/2     Let not your Worships thick skin be too sensible that we thus Tan your Hide.

The discoloration of the skin in the allusion can be explained with the use of tannin in the traditional tanning process which gives the distinctive color of the tanning. Here is an explanation from the book How it Works: Science and Technology, Volume 9:

Traditional tanning methods, which impart a characteristic color to the skins and convert an otherwise perishable material into a stable and nonperishable hide, traditionally used vegetable tannins leached from the leaves of shrubs and trees, such as quebracho and sumac leaves, and the bark of oak to tan the skins. Modern processes use concentrated vegetable extracts instead. The process was discovered early in human history, probably when a raw skin was left soaking in a pool of water into which tannins had coincidentally leached from fallen leaves.

Vegetable tanning produces the tan color still seen in sole leather and some harness and industrial leathers, such as belting. Apart from these applications, vegetable tanning is not widely used as the principal tanning agent, except in countries such as India. The process is slow: heavy sole leather, for example, can take several weeks to tan as the hides move progressively through tan liquors of increasing strength.

The discovery of the chrome tanning process early in the 20th century revolutionized leather making by introducing a mineral tanning process that can tan leathers in hours. Most shoe upper leather is now tanned in this way, and the process can be recognized by the blue-green color of the undyed leather. Chrome-tanned leathers were found to be more heat resistant and easier to waterproof and, in some cases, could even be made fully washable.

The flow diagram of the traditional tanning process from Davarg leather company:

While it may seem obvious now that the phrase 'tan your hide' "takes its origins from the way that leather is processed", the historical evidence suggests that, insofar as the phrase does take its origins from that process, that is the least significant contribution to the original meaning. The context of early uses suggests, rather, that the phrase is an elided version of this claim:

I'm gonna flay you, then tan the hide.

Early uses do not necessarily express the first part ("flay you") outright; it was (and is), however, understood that a 'hide' cannot be tanned until the animal has been skinned.

The context of the first attestation in the OED,

Let not your Worships thick skin be too sensible that we thus Tan your Hide.

[from around 1670, in Expostulatory letter, A mild, from the plaindealing farmers of the neighbouring villages to the men of Buckingham]

is not available to me, so I must set it aside without comment. The second OED attestation, from the 1732 play The devil to pay (Charles Coffey),

...to Work, to Work, come and spin, you Drab, or I'll tan your Hide for you....

follows in the train of an earlier beating:

Lady. ...What Rascal are you?
Job. This is amazing, I never heard such Words from her before. If I take my Strap to you, I'll make you know your Husband....
....
Job. ...to Work, to Work, come and spin, you Drab, or I'll tan your Hide for you....

Coffey's play The devil to pay itself follows, too closely, in the train of an earlier beating, as encountered in The devil of a wife, a play by Thomas Jevon. Jevon died in 1688; his play was published in 1735, yet Coffey's 1732 play The devil to pay obviously owes...overmuch...to Jevon's play:

Job. Come, come, you Quean, I'll make you leave your fooling, come to your Spindle, or else I'll lam your Hide, you were ne'er lamm'd so since you were an Inch long.

In Jevon's play, "lam" (and "lamm'd") are used with the meaning shown in the 1825 A glossary of north country words in use, by John Trotter Brockett:

Lam, Lamb, to beat soundly. "Aw'l lamb yor hide."

"Lamb them, lads; lamb them!" — a cant phrase of the time, derived from the fate of Dr. Lambe, an astrologer and quack, who was knocked on the head by the rabble in Charles the First's time.
Peveril of the Peak, vol. iv. p. 132.

Plainly, 'tan' in the early use found in Coffey's play is being employed with the metonymic sense of 'beat'; already, before 1732, little of the literal sense of 'to tan', that is, "to cure leather with tannins", remains in Coffey's use, which seems to have been, um, 'lifted', more or less directly, from Jevon's earlier (before 1688) use 'lam' of in the sense of "beat".

The same metonymic distillation of 'tan' into the sense of 'beat' as was seen in Coffey's 1732 play can be found in another 1732 publication, a translation of Molière's The Miser, where the translation of je vous rosserai is "I shall tan your Hide." The French verb rosserai translates literally as "whip", "flog", "trounce", "beat up", etc. It is, however, beyond my expertise to say which meaning was likely in French of the 1600s.

Doubling back to Brockett's 1825 glossary, and an 1830 publication by Robert Forby (Vocabulary of East Anglia, a vocabulary which the title page advertises as having been collected in the last two decades of the 1700s), I observe that two other survivals (along with 'tan your hide' and 'lam') from the 18th century suggest the close association of 'tan' with 'flay', 'flog', 'thresh' — that is, the 'tan' in 'tan your hide' is the promised result after the acquisition of your hide by a severe beating. Those survivals are 'to hide' and 'a hiding', in the sense of 'to beat' and 'a beating' respectively.

Hide, to beat. "I'll hide your jacket."

[From Brockett, 1825: note that 'jacket' in Brockett's quote is used in the sense of "skin".]

HIDE, v. to thresh; to curry the hide. BR.
HIDING, s. a beating.

[From Forby, 1830: Forby's "BR." credits Brockett's definition; 'thresh' is what OED says is the "earlier and etymological form of THRASH v."]

None of the foregoing is conclusive with respect to my claim that, after examining the historical evidence given above and more, 'tan your hide' referred not so much to discoloration of skin as to a beating so severe as to flay the recipient, followed by a promise to tan the hide removed by the flaying. Either explanation of the origin of the term (that it refers to skinning followed by curing, or that it refers to simple discoloring) might serve as well as the other; however, in the absence of direct historical evidence contradicting my observations, mine is the more likely explanation of early use of the phrase.