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Merrian Webster defines clout

4 : PULL, INFLUENCE

political clout

She parlayed her box-office clout to wealth and independence
— B. S. Pierre

Etymonline explains that clout:

Sense of "personal influence" is 1958, on the notion of "punch, force."

When and where did this sense first emerged?

According to the Random House Dictionary there is an early usage instance in the mid-19th century of clout used in political context. But its usage appears to have started in Chicago in the mid-1900:

The Random House Historical Dictionary of American Slang suggests it was in New York, citing an 1868 letter Walt Whitman received from his brother, Thomas Jefferson Whitman, about some Brooklyn guys who “always think they are going to be deprived of office and ‘clout.’” But it’s curious that the term barely surfaced at all for another eighty years.

Political clout” appeared in the Tribune for the first time in 1946, in a story about hoodlums seizing control of the Bridge and Structural Iron Workers Union. One of the alleged thugs, Matt Breen, reportedly told a union official:

• “It’s tough, Tom, that you can’t understand that I’m the boss now over all iron workers. I’ve got a political ‘clout’ that’s bigger than you imagine.”
  

Over the next 40 years, “clout” pulled ahead of “pull” in Chicago’s vocabulary. “Pull” must have started to sound bland in comparison with this more visceral and menacing word. The Trib referred to “political clout” 762 times between 1946 and 1985, compared to 121 instances of “political pull” over that same period.

(www.chicagomag.com)

Fisticuffs and Sport

Clout as an uncountable noun meaning power or influence, especially in politics or business, is a metaphorical extension in the late 1950s of its original meaning as a strong blow, strike, or hit:

Yes, rot him! He gave me a cursed clout o' the jaws, and called me a coward, … — William Dunlap, The Africans, 1811. COHA

Rather than directly derived from random acts of physical violence, however, the new meaning was likely mediated through the word’s earlier extension into the world of sports: to clout opponents is to defeat them. A clout was a strong punch in boxing or a long hit in baseball, usually scoring. Sports reporters would occasionally use the word to describe a powerful drive in golf or tennis. The common denominator is strength and power: politics or business was just another game.

To say that the carnival of clout presented an the feature performance of the dual bill was a great banket ball exhibition would bo cutting the throat of truth to some degree. — Journal News (Nyack NY), 4 Jan. 1935.

Joe Louis, king of clout, arrives from the Midwest tomorrow to launch his 1940 campaign to begin training for his ninth defense of the world heavyweight championship against Arturo Godoy of Chile at Madison Square Garden on Feb. 9. — Jack Cuddy, “In This Corner” (syndicated column), San Bernadino Sun 12 Jan. 1940.

Mickey Mantle, baseball’s grand champion of clout, Monday night was named winner of the seventh annual S. Rae Hickok Professional Athlete of the Year Award and the 810,000 diamond-studded, gold-buckled belt which goes with it. — Daily Illini (ind. student paper, Univ. of Ill.Champaign-Urbana), 22 January 1957.

Using the word in this fashion, i.e., as an uncountable noun, opens the door to clout becoming an attribute or quality one could have instead of an action one performed.

Ann Landers

A search of digitized American newspapers yielded what may be the first occurrence of the new usage, some months before the 1958 date Etymonline suggests. A 15-year-old girl, signing her letter “Ragweed Ruth,” complains to syndicated advice columnist Ann Landers (Esther Lederer) that her mother kept bringing flowers and plants into the home to which she is allergic. Ann replies:

Take your problem to your family physician. He'll have more clout than anyone. If HE suggests that Mother clear away the jungle, she'll probably listen. — “Ask Ann Landers” (syndicated column), San Bernardino Sun 64/25, 30 Sept. 1957.

Both Lederer and her twin sister, Pauline Phillips, who wrote the quite similar “Dear Abby” column, were noted for their use of colloquial forms and slang, so the expression might not be that much older than its appearance in Lederer’s column. Considering Lederer’s wide circulation, many Americans who might not have been familiar with the usage would have learned it from her.

Mobsters

Curiously enough, in the jargon of organized crime, a clout was someone on the mob payroll:

Harry Cane, brother of former West Coast mobster Mickey Cohen, testified that the racket could not exist “without a clout at the banks and a clout at the FHA.” Cane explained that “clout” is an underworld term for a contact who can be bribed. — San Bernardino Sun 61/15, 17 Sept. 1954.

To have clout at the Federal Housing Administration to further their home remodeling and repair racket — funds were diverted — the mob needed clouts.