This is just a placeholder answer while look for the complete connection to the phrase "cheaper by the dozen".

We know that englishmen in the colonies and what would become the "United States" forced prisoners of war (what englishmen refer to as "slaves") to have sexual intercourse with their mothers, in an effort to produce more prisoners of war, for free labor, fun, glory, material gain, and experimentation, see [_Medical Apartheid
The Dark History of Medical Experimentation on Black Americans from Colonial Times to the Present_ by Harriet A. Washington][1]. Forcing young prisoners of war to impregnate their mothers is but one of the horrendous practices of englishmen in the western hemisphere. Without such experiments what is referred to "modern medicine" would not exist. If you find the time, browse the historical medical records of the University of Chicago.

That is the origin of the term **motherfucker** from which the **cheaper by the dozen** phrase was used to refer to the offspring of such forced impregnation.

The late [Dick Gregory][2] revealed many of these historical facts before their passing. It has been some time since last reviewed the actual phrases usage. Am not entirely certain if Dick Gregory is the one and only source of the meaning of that phrase, within the context of the offspring of male prisoners of war in the western hemisphere being forced to impregnate their mothers to produce more prisoners of war.

It is not surprising that anglophiles deny, or refute such origins of terms in the english language. 

Though for an individual who is not an englophile, it is common knowledge that english is first and foremost an **equivocal language**, intended to be used for deception, capable of having more than one meaning for each word or phrase. There is no such thing as "good" or "proper" english. The language is a result of conquest by the Normans, Romans, whores, convicts, pimps, murderers, imperialism and several hundred years of institutional white supremacy.

In any event, this [Dick Gregory - On Slavery, Reparations and Hurricanes][3] 


> ... we can't have no more. How we gonna do this?... So he made me, 14
> years old, put a sock over my head, and have sex, fuck my mama...
> 
> ...cause she didn't want him to get made and start killing the
> slaves... 
> 
> ... and so, I had to screw my mama man...
> 
> ... That's where the word **motherfucker** comes from and then white
> boys shit and they hated the word until they got around black folks...
> 
> ... and now you go to a white movie and they say mothafucka before
> they finish running the credits from the movie...

is a brief introduction to the emergence of the phrase "cheaper by the dozen" being used to refer to the offspring of so-called "black" or african women in the western hemisphere being force to be impregnated by their sons, the result of which was often birth defects, which were still valuable "property" for those englishmen who bought and sold human beings. The interview provides accounts for the origin of the terms **honky** and **motherfucker**. Will edit the answer to address specifically how the **motherfucker** history resulted in **cheaper by the dozen**. 

Note, that same interview describes the origin of the term **honky**, which is derived from english, or so-called "white" men literally honking the horn of their vehicle outside of the whorehouse they were visiting to buy sex from so-called "black" women.

See also [The History Of Male Slave Rape (Buck Breaking) And The Word MotherFucker][4].

----------




[The History Of Male Slave Rape (Buck Breaking) And The Word MotherFucker][7]

> ...especially in Jamaica, they were doing a process called "buck
> breaking" where the white supremacist slave owner or the white
> supremacist overseer would literally rape black men in fron tof the
> black population in order to break his spirit, in order to break him
> down as a man, in order to show dominance against him, in order to
> show the rest of the black population that this is not your leader I
> just made your leader submit to me sexually. 
> 
> It was a matter of power and control and domination, and they would
> call it "buck busting" but it was really "butt busting".
> 
> 
> Slavery continued until 1865... for about two generations, right, so
> how do you reconcile that?
> 
> You can no longer bring in Africans but you still have the business of
> slavery, so they still needed Africans to do the work down south,
> especially after the cotton gin was invented

(which Dick Gregory also discloses was based on the inventions of one or more African prisoners of war; whom that Whitney witnessed at or got wind of at plantations. The invention is
attribution solely to Whitney per U.S. Patent, though is still disputed by some today; some credit the invention to a European woman)

> So you had the creation of breeding farms. Two of the largest slave
> breeding farms in the United States were on the eastern shore of
> Maryland, and right outside or Richmond, Virginia. The literally bred
> black people like cattle.  
> 
> They would have  a strong black man have sex with a healthy black
> woman.That woman could be his mother, his sister,  his aunt, his
> cousin. It didn't matter. Because the end product was product a child
> that I can sell, bodies that I could sell and ship down to
> Mississippi, Alabama, Georgia, South Carolina, North Carolina. It was
> a business.
> 
> We had breeding farms in the United States... Even if you were mother
> and son, they would mate you... **And so I tell a lot of my patients
> and a lot of my friends, you gotta stop using the "MF" word because
> that was a description of  what actually happened when they would put
> the paper bag would go over the head  to put one breeder against
> another when they were related.**

[The Origins of The Dirty Dozens][5]


> The term the dozens is believed to refer to the devaluing on the
> auction block of slaves who were past their prime, who were deformed,
> aged or who, after years of back-breaking toil, no longer were capable
> of hard labor. These enslaved human beings often were sold by the
> dozen. In _African American Oral Traditions in Louisiana_, African
> American author and professor Mona Lisa Saloy writes:  **“The dozens has
> its origins in the slave trade of New Orleans where deformed
> slaves—generally slaves punished with dismemberment for
> disobedience—were grouped in lots of a 'cheap dozen' for sale to slave
> owners.** For a Black to be sold as part of the **'dozens'** was the lowest
> blow possible.”


[African American Oral Traditions in Louisiana][6] By Mona Lisa Saloy

> "The Dozens" are an elaborate insult contest. Rather than insulting an
> opponent directly, a contestant derides members of the opponent's
> family, usually his mother. **The dozens has its origins in the slave
> trade of New Orleans where deformed slaves—generally slaves punished
> with dismemberment for disobedience—were grouped in lots of a "cheap
> dozen" for sale to slave owners. For a Black to be sold as part of the
> "dozens" was the lowest blow possible.**



  [1]: https://en.wikipedia.org/wiki/Medical_Apartheid
  [2]: https://en.wikipedia.org/wiki/Dick_Gregory
  [3]: https://www.youtube.com/watch?v=tF5mfhW1qBo
  [4]: http://The%20History%20Of%20Male%20Slave%20Rape%20(Buck%20Breaking)%20And%20The%20Word%20MotherFucker
  [5]: http://www.morganparkcps.org/ourpages/auto/2010/5/24/59616133/The%20Dozens.doc
  [6]: http://www.louisianafolklife.org/LT/Articles_Essays/creole_art_african_am_oral.html
  [7]: https://www.youtube.com/watch?v=MWigLcAkZCI