Frederick Marryat, in Poor Jack (1840), thought the spelling should be P-jacket: “A short P-jacket (so called from the abbreviation of pilot’s jacket),” he wrote, “reached down to just above his knees.”
But Marryat was wrong.
The original first element was pee, back in the fifteenth century, taken from Dutch pi j, and that was the name of a kind of coat made of a coarse cloth and worn by men.
Coat and name died out in England, but were revived in America in the early eighteenth century, first as pee-jacket and later in the present form, both apparently from Dutch pij-jakker of the same meaning, a short, double-breasted coat of thick woolen material, worn by sailors in severe weather.