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.
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.
