Green’s Dictionary of Slang

stepinfetchit n.

1. (US, also step-and-fetch-it) an old man with a lively step [lit. ‘step and fetch it’].

[US]G.D. Chase ‘Cape Cod Dialect’ in DN II:v 301: step-and-fetch-it, n. An old man with a spry gait.

2. (US black) a subservient black person, fitting willingly into the stereotyped and inferior image refined by generations of white supremacy[nickname of Lincoln Perry (1892–1985), who specialized in playing stereotypical ‘dumb nigger’ roles for Hollywood; he chose the nickname after a winning racehorse].

[US]E.E. Landy Underground Dict. (1972).
UPI 22 Sept. n.p.: Representative Henry B. Gonzalez called Samuel R. Pierce, Jr., the Secretary of Housing and Urban Development, a ‘Stepin Fetchit,’ and although Mr. Pierce termed that epithet ‘vile, abusive and racist,’ the Texas Democrat refused to apologize [R].
[US]Wolfe & Lornell Leadbelly 128: [A]fter [John Lomax] wrote up the incident for Negro Folk Songs he decided to delete it from the final draft, perhaps feeling that it made Leadbelly seem like an accommodating ‘Stepin Fetchit’ .

3. attrib. use of sense 2.

[US]N.Y. Times 12 Mar. 125: Mike Evans, who plays the young black neighbor Lionel, is obliged by his role to affect an occasional Stepinfetchit manner.
[US]P. Beatty Tuff 39: The missing link between prehistoric Stepin Fetchit man and the genetically engineered Denzel Washington that fossilized him.

4. (US) used of anyone, race irrelevant, subservient.

[US]D. Lehane A Drink Before the War 5: Brian Paulson [...] waited until Mulkern sat back down before he did, and I wondered if he’d asked permission before he sweated all over my palm too. [...] They said he had a mind, though, honed by years as Mulkern's step-and-fetch-it.