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My family settled on the Cape in the late 1600s or early 1700s. According to Deyo's history of Barnstable County, the family came from Isle of Guernsey. A few years ago I ran a DNA query against the Sorenson Molecular Genealogy Foundation (SMGF) database and found a match with the name Le Sueur. The entry indicated the family came from the Isle of Jersey (next door to Guernsey). Le Sueur is old French for shoemaker, but in modern French means "sweat."
Simeon L. Deyo, History of Barnstable County Massachusetts 1620-1890 (New York, H.W. Blake, 1890), page 821:
James Swett -- This family name was transplanted in 1630 from the Isle of Guernsey, in the English Channel, to Newburyport, in the New World; and in 1670 two brothers, descendants of the name, came to the Cape, Benjamin, one of them, settling in Wellfleet, and Noah, the other, in Truro. They were seafaring men, and from them have descended the family in Barnstable county. Benjamin, grandson of the first of that name who settled here, married, and from him descended the subject of this sketch.