Learn English – Where did the term “cheesy” come from

According to the OED, the term OK began its days as a humorous initialism “apparently derived from the initial letters of oll (or orl) korrect, jocular alteration of ‘all correct’ ”, when it was first seen almost 200 years ago in the United States, way back in 1839.

It seems that this sort of off-kilter formation was considered quite funny at the time: “an instance of a contemporary vogue for humorous abbreviations of this type” per the OED.

By 1840, this use was “greatly reinforced by association” with another identical initialism O.K., this one derived from the nickname Old Kinderhook adopted by Martin Van Buren during his 1835 electoral campaign for the U.S. presidency. The corresponding verb was soon null-derived¹ from this initialism around 1882.

The OED further notes (with bold emphasis added in this post for clarity) that:

Other suggestions, e.g. that O.K. represents an alleged Choctaw word oke ‘it is’ (actually the affirmative verbal suffix -okii ‘indeed, contrary to your supposition’), or French au quai, or Scottish English och aye, or that it derives from a word in the West African language Wolof via slaves in the southern States of America, all lack any form of acceptable documentation.

The OED further states that “Competing theories as to the origin of the expression have been in evidence almost since its first appearance”, and then provides several early completing theories in support of that assertion.

Footnotes

1. Null derivation, also known as zero derivation, is when a word is conscripted unchanged into use for a part of speech that’s different from the customary one. It has no derivational affix and so is said to be null derived, such as when we null-derive nouns from adjectives in The Good, the Bad, and The Ugly. A clearer example of this is the classic refrain that “verbing weirds language”, which features two instances of null-derivation: not only does it null-derive a new verb “verb” from its noun and then uses its verbal -ing inflection as a subject, it also null0derives a new verb “weird” from its adjectives and then uses the new verb’s third-person singular inflection.

I've got a possible interpretation, for which however, I'm afraid there is actually little hard evidence (but considering the scarcity of etymology studies dealing with prostitution professional vocabulary, this is hardly surprising). However if you connect the dots, it kind of makes sense.

For each dot, in the conjecture below, I will add a confidence level (abbreviated as CL), so that hopefully other contributors might fill the gaps.

Here it goes anyway:

It all comes from... Surprise, surprise.... French argot (slung).

1. "trique" in popular French is a word for a wooden stick (CL 100%). French donkey's are sometimes motivated using "des coups de trique". It is believed to come from Northern French dialectal "estrique" and is akin to "strike" in English, "streik" in German and so on. Also gives "tricoter" (to knit) in French.
2. "avoir la trique" or "triquer" means to have an erection (CL 100%).
   Passing the boundary between popular and argotic here.
3. By extension "triquer" or "trequer" means, for a man to make love, in a careless/bestial way to his partner. (CL 100%). Please refer to a famous novel named "Prostitution" by Pierre Guyotat, easy to find on the web. Just Google for "Guyotat triquer" and you should net a large number of hits.
4. The verb "triquer" used as "to have sex with a prostitute" was particularly common in the world of French prostitution in the previous century at least (CL 50%). Can't back this from personal experience, I'm afraid ;-).
5. The idiomatic expression passes in the English language somehow (CL 20%).
6. A trick in English in the context of prostitution has both the meaning of a customer or the act itself. (CL 100%).
7. To "turn tricks" is to engage in acts of prostitution with "Johns" or "Tricks".

So you see, this is a possibility but there are a few gaps which I'm not able to fill with certainty.

Edit
Since this post was composed (more than one year ago) and as I researched the world of the French Impressionists, I came across additional info concerning the step in which the expression passes into English.
It is a well documented fact that the French industrial revolution was accompanied as everywhere else, by rural exodus, poverty, and an increase in the levels of urban prostitution. It is also possible to show that a proportion of French prostitutes emigrated to the US and various other destinations (even Australia) at that time (end of the 19th Century). Conversely, one can find examples of "petits femmes de Paris" having risen to a certain level of fame and wealth in the US at the time.
In summary, the possibility that the expression passes into English now seems less conjectural to me.