The story
There were and are many roads of this name in the American South. The meanings are derived from the 1932 novel, Tobacco Road, by Erskine Caldwell and the 1933 play and 1941 movie derived from it. Caldwell does not use the term "Tobacco Road" to refer to the region or place, only to the roads themselves. According to Caldwell, the roads were created by rolling thousands of tobacco casks over them, over many decades. In the Savannah Valley of 1932 there were "scores" of these roads, ranging up to 30 miles in length. The casks were known as hogsheads, were roughly 48 inches by 36 inches and weighed about 1000 pounds once filled with leaves.
Etymology from Wiktionary, CC BY-SA 4.0.