I'm not aware of any biography of Langdon Cheves, Jr. you will find some of his correspondence and oher papers in the Langdon Cheves, Jr. Papers, and in the Langdon Cheves I Papers, both at the South Carolina Historical Society; a few references and other matters related to him in the Cheves-Wagner Family Ppaers, Southern Historical Collection, University of North Carolina and perhaps the best bet is a biography of his sister in the Mrs. Augustine (Louisa McCord) Smythe Papers, South Caroliniana Library, University of South carolina. This is a typescript, however. There are a few references to him in the study of Mrs. McCord published by University of Missouri Press a few years ago, but it focuses on the life and attitudes of a Southern female intellectual and her ideas on slavery, so it is not by any means a study of Langdon Cheves, Jr.
The correct (or Carolina) of the surname is CHE (as in Chevrolet)- vis, with the stress on the first syllable; the same as in Chevis Regal liquor.