In the book I am reading the author said that sweetback means a man who lives off the earnings of his woman. I haven't heard this before and couldn't find it online or in a dictionary. Have you heard it?

From the OED Online:

sweetback n. U.S. slang a woman's lover, a ladies' man; a pimp; also sweetback man (cf. sweet man n. below).

1929    in P. Oliver Screening Blues (1968) vi. 206   Had a man, good old sweetback.
1935    A. J. Pollock Underworld Speaks 117/2   Sweet back, a pimp.
1950    R. P. Blesh & H. Janis They all played Ragtime ii. 39   The dapper, foppish ‘macks’ or ‘sweet-back men’..got their gambling stakes from the girls.
1974    Black World Sept. 25/2   Long Black Song tells us, here in the 1970's, that the days of darky entertainers, superflies, sweetbacks, and Melindas, if not over, are numbered.

sweet man n. U.S. slang = sweetback n. above.

1942    L. V. Berrey & M. Van den Bark Amer. Thes. Slang §443/5   Beau,..sweet man.
1942    L. V. Berrey & M. Van den Bark Amer. Thes. Slang §508/3   Pimp..sweetman.
1952    S. Selvon Brighter Sun ii. 21   Look how Ah take up meself and leave sweetman life in town.
1959    V. S. Naipaul Miguel St . xi. 118   Eddoes was a real ‘saga-boy’. This didn't mean that he wrote epic poetry. It meant that he was a ‘sweet-man’, a man of leisure, well-dressed, and keen on women.
1972    J. Maryland in T. Kochman Rappin' & Stylin' Out 211   Damn, Rev., that's some real cruel shit, suggesting a sweet man [pimp] be iced.

In the book I am reading the author said that sweetback means a man who lives off the earnings of his woman.

Well, I've seen the movie Sweet Sweetback's Baadasssss Song (link) by Melvin Van Peebles, and the main character is kind of a pimp, so I guess I have. It was made in '71, so I guess it's been around in AAVE (link) for a while.

Interesting, Tinman & z. I didn't find much online.

I really need to do something about getting online OED again.

I suppose a pimp could be similar to a sweetback, though, I see a pimp as doing a little work (albeit not that upstanding of work!).