Entry in progress—B.P.
 
Wikipedia: List of mammals of SOuth Carolina
Mustelidae
 
. Least weasel (Mustela nivalis)
. Long-tailed weasel (Mustela frenata)
. Mink (Mustela vison)
. North American river otter (Lutra canadensis)
. Spotted skunk (Spilogal putorius)
. Striped skunk (Mephitis mephitis)
 
Google Books
April 1845, Cincinnati Miscellany (Cincinnati, OH), pg. 240:
S. Carolina, Weasels.
 
Chronicling America
23 August 1845, Ripley (MS) Advertiser, pg. 1, cols. 4-5:
NATIONAL NICKNAMES.—It will be seen by the following from an exchange paper that the people of every state have nicknames, and some very curious and ludicrous ones:
 
The inhabitants of Maine, are called Foxes; New Hampshire, Granite Boys; Massachusetts, Bay Staters; Vermont, Green Mountain Boys; Rhode Island, Gun Flints; Connecticut, Wooden Nutmegs; New York, Knickerbockers; New Jersey, Clamcatchers; Pennsylvania, Leatherheads; Delaware, Muskrats; Maryland, Craw-Thumpers; Virginia, Beagles; North Carolina, Weasels; Georgia, Buzzards; Louisiana, Creowls; Alabama, Lizzards; Kentucky, Corn crackers; Tennessee, Cottonmanics; Ohio, Buckeyes; Indiana, Hoosiers; Illinois, Suckers; Missouri, Pewks; Mississippi, Tadpoles; Arkansas, Gophers; Michigan, Wolverines; Florida, Fly-up-the-Creeks; Wisconsin, Badgers; Iowa, Hawkeyes; N. W. Territory, Prairie Dogs; Oregon, Hard Cases.
 
Chronicling America
4 July 1860, The Spirit of Democracy (Woodsfield, OH), “National Nicknames,” pg. 1, col. 7:
The inhabitants of Maine are called Foxes; New Hampshire, Granite Boys; Massachusetts, Bay Staters; Vermont, Green Mountain Boys; Rhode Island, Gun Flints; Connecticut, Wooden Nutmegs; New York, Knickerbockers; New Jersey, Clam Catchers; Pennsylvania, Leather Heads; Delaware, Muskrats; Maryland, Claw Thumpers; Virginia, Beagles; North Carolina, Tar Boilers; South Carolina, Weasels; Georgia, Buzzards; Louisiana, Creowls; Alabama, Lizards; Kentucky, Corn Crackers; Ohio, Buckeyes; Michigan, Wolverines; Indiana, Hoosiers; illinois, Suckers; Missouri, Pukes: Mississippi, Tad-Poles; Florida, Fly up the Creeks; Wisconsin, Badgers; Iowa, Hawkeyes; Oregon, Hard Cases.
 
25 July 1864, Indianapolis (IN) Daily Journal, “National Nick-Names,” pg. 4, col. 2:
South Carolina…Weasles
 
Google Books
June 1865, The Wisconsin Journal of Education, pg. 328:
The following are the “nicknames” of the native inhabitants of the different States:
... South Carolina, Weasels; ...
 
Google Books
U. S.
An Index to the United States of America
Compiled by Malcolm Townsend
Boston, MA: D. Lothrop Company
1890
Pg. 80:
NICKNAMES APPLIED TO THE PEOPLE OF THE STATES.
(...)
South Carolina…Weasels...Backwoods application to natives.
 
Google Books
Universal Dictionary of the English Language
Edited by Robert Hunter and Charles Morris
New York, NY: Peter Fenelon Collier, Publisher
1898
Pg. 5344:
South Carolina. Weasels (a backwood title for the natives).