PAR #: 11483316
Location: Gibson County, TN • Year: 1833

Abstract: Residents of Gibson County request that Zachariah Roberson, a free man of color, be permitted to bring part of his family from North Carolina into Tennessee. "We state that he & his family have behaved them selves with propriety, industry & honesty."

PAR #: 11483317
Location: Gibson County, TN • Year: 1833

Abstract: Free black Zachariah Roberson asks that members of his family living in North Carolina be permitted to immigrate to Tennessee. In April 1831, Roberson had purchased a tract of land in Gibson County for $960, but a short time later the legislature passed a law prohibiting free blacks from entering the state.

I see no evidence that he is in the state in 1840.
It might be possible that he is the free black found in Arkansas, since Roberson is often spelled Robinson:

1840 cenusus:

Name: Zachariah, Robinson
Township: Saline
County: Hempstead
State: Arkansas
Roll: 18
Page: 170