To gouge in AmE means to overcharge or swindle someone. The expression price-gouging, for instance, refers to the practice of unfairly charging customers too high prices.
How did the AmE sense evolved from the original one? Etymonline suggests that it developed around the first part of the 19th century but adds no other details.
Notwithstanding the OED's first occurrence date of 1875 for gouge as a verb meaning "to cheat or impose upon" (cited in Greybeard's answer), I came across an instance from three decades earlier that seems to use the verb in a similar sense. From I. Richmond Barbour, The Silk Culture in the United States (1844):
Yet this [the sudden decline in prices for mulberry tree contracts during the initial stage of the economic crisis of 1839] was only the beginning of the trouble. There was at this time [October 1839], interest enough, and confidence enough in the Silk business, in the community, to have sustained this shock, severe as it was, if there had been nothing more, or nothing worse. But in this critical juncture of affairs, a juncture demanding the utmost coolness, and firmness on the part of all interested,a universal and uncontrolled panic seized the great body of the smaller dealers—The men who had invested from $50 to $500, and who constituted the great numerical majority, perhaps nineteen-twentieths of the whole number interested in tress. As if by some unseen, uncontrollable power, these men were every where seized with a fixed determination to get rid of their trees at any price, and on any terms. Talk with them? As well talk with the whistling wind. Explain to them the financial causes that had been at work to produce this temporary depression on this, and on all business? As a class, they were too ignorant of general business to understand any of these questions. Unfold to them the essential merits of the Silk business, the great principles om which it is based, as a permanent business of the country? It was too late in the day to teach them this neglected lesson. Selling trees, selling trees—this was the only thing their eyes had been fixed upon, and now that trees had fallen 25 to 50 per cent in a few weeks, they were determined to be rid of them at all events. No instruction, no remonstrance, no intreaty was of any avail. Fear had taken full, and uncontrolled possession of the mind; and every day's rumor only extended and augmented the panic. Hence they at once began to run upon each other. If A. offered his trees at 20 cents, before night B. offered his at 18, and the next day C. had as good trees as ever grew at 16, and would even take less, rather than lose a sale, as he wanted money. So the alarm spread like wild fire. They run from one to another trying to gouge each other, and from neighbor to neighbor, betraying the utmost anxiety, and resorting to all manner of devices to effect sales. Wagons loaded with trees were driving, Jehu-like, from town to town, and in every direction, each load of course cheaper and better than any that had gone before, or would come after.
This certainly reads like an instance where gouge is being used to mean "to cheat or [economically] impose upon." It is also interesting that the author italicizes the word in this occurrence, as if to emphasize its novelty or special descriptive force.
Three years later comes this instance from "Uniformity in the Size of Loaves" in Yankee Doodle (New York City, August 7, 1847):
Some wiseacre in the Board of Aldermen, a short time ago proposed an ordinance that should provide for the size of a Loaf of Bread. A measure only calculated to give a rogue a chance to carry on his depredations under the cloak of perfect legality, and blind the community to the sober reality of their cheatery. The quality of Bread is a far easier means to gouge the customer than the mere weight or size. But these small Law-makers, are never so well contented as when twisting their straws and making their remarks, and offering their resolutions.
And three years after that, from a speech by Volney Hascall, of Kalamazoo, Michigan, on July 15, 1850, reproduced in Report of the Proceedings and Debates in the Convention to Revise the Constitution of the State of Michigan (1850):
When printers at the capital are compelled to do the State work in a proper and workmanlike manner, and receive therefor healthy and fair prices, this will have its influence throughout the State, and country printers will not be compelled to do weork at the miserable pittance which has been bid by State printers, for two or three years past; and who, in order to live by their contracts, have been compelled to gouge the State in every possible manner. I think, sir, the craft will soon realize the benefits of this stable and healthy manner of conducting the public printing. I hope the good sense of the Convention will see the impropriety of striking out.
And that same year in remarks by Mr. Gerry in the House of Representatives on September 23, 1850, reproduced in The Congressional Globe (September 24, 1850):
Now I do not see that there is any claim here either in law or equity. The city of Brooklyn has no right to complain in her corporate capacity. If there be claims for damages, individuals only can prefer them—the government. I am well persuaded here is an attempt to gouge the Government out of $50,000, and for one I am for resisting.
And two years after that, from a select committee report reported on March 24, 1852, reproduced in The Journal of the Senate of the State of Ohio (1852):
It is reported, and much of it on authority of which your committee is bound to believe, that a systrem of fraud and peculation has characterized the proceedings of one of the State land officers and other gentlermen at [the town of] Defiance. It seems that it has been usual with certain persons in the vicinity of the land offices, to furnish money to irresponsible individuals who would make the oath of settlement and get the land at half the appraised value—a privilege which the law extends to actual settlers—and that the land, or a large portion of it, would, through a private arrangement, revert to these individuals who furnished the money; thus enabling them to become owners of the land at half price [without actually settling on it], and to gouge the State out of the other half. ... This land is lying in the vicinity of Defiance, and was appraised at an average value of about three dollars and fifty cents per acre, making about five thousand dollars which the State of Ohio been defrauded out of by mere speculators, or, as they are more familiarly known, "land sharks."
And five years after that, from a letter titled "Quackery," dated July 1857, to The Medical and Surgical Reporter (Burlington, New Jersey, August 1857):
Quack medicines still live. Harrison's lozenges are all the go now. Taken at night, and through by daylight—no stoppages. The proprietor has managed to get a recommendation from one of the most respected men of our profession in Boston, to one of the most respected physicians in New York. Of course, both gentlemen are sold; their names are paraded before the public with every box, and stuck under the front door on every street. These lozenges are said to be composed simply of iron and senna, which I don't simply believe. Why the profession are willing to sustain any medicine-monger, who advertises nostrums, I cannot conceive. By doing so, they discourage the honest druggist, and encourage the quack druggists to gouge the public.
And that same month and year, from "Did You Ever" in American Farmers' Magazine (New York City, August 1857):
We are very far from wishing to compare all who seek the farmer's patronage with this man [a person trying to sell farmers patented farm equipment of dubious practical value for exorbitant sums]. There are hosts of implement makers, seedsmen, manure vendors, and patentees, who are willing to deal fairly. But there are others, men who seem to live by honest labor, and to become rich by slow degrees, who are seeking to gouge the laborious, home-keeping cultivators of the soil. They love the farmer no doubt; but they love his money-bag a great deal better; and they are not satisfied to deal with him on terms equally beneficial to both parties; but are managing to make more rich in a year by their trade, than he can in life by constant labor. The evil is a great one, because it forces the farmer to be so on his guard against imposition, that he almost unconsciously falls into an attitude of resistance to real improvements. This unceasing scheming in our cities to gouge the farmers is what more than any other thing now impedes the progress of agricultural improvement in the whole country. It is a crime against patriotism and humanity, and ought to be intensely detested.
It therefore seems that the verb gouge, in the "cheat or impose upon" sense, was in use in the United States by 1844 and was fairly well established by 1857.
OED:
Gouge in the sense given was, at first, the noun used metaphorically:
3. U.S. colloquial. a. The action of gouge v.; a scooping out. b. A cheat, swindle (cf. gouge v. 4). ‘Also, an impostor’ (Cent. Dict.).
1845 This is a clean, plain gouge of this sum out of the people's strong box. New York Tribune 10 December
1887 Another ‘gouge’ was to charge the women a nominally cost price..while, as a matter of fact, it was got..for considerably less. American vol. XIV. 344
Note the idea of a metaphorical painful and deceitful extracting of value.
Gouge (v.) was first recorded in 1875:
**4.**U.S. To cheat, impose upon. Also absol. 1875 The man's a perfect Jew—or a perfect Christian, one ought to say in Venice; we true believers do gouge so much more infamously here. W. D. Howells, Foregone Conclusion (1882) iii. 69
1885 He's regularly gouged me in that ere horsehair spekilation. B. Harte, Ship of '49 i
The sense of noun and verb comes across of one of the immoral and painful sticking of a sharp instrument into a person and levering something of value out of them.
