I suspect that Martha is the female age 5-9 in the household headed by Rebecca Pettit in 1840, but I don't know whose widow Rebecca is. Morgan Co. land, estate, or guardianship records may help.

1850 census of Morgan Co. lists on p. 107, household #288, with the family of William M. Fugett (29) and wife Hannah (29), Martha Petitt, age 16. Children of William and Hannah are James, 6; Rebecca, 3; Lucinda, 1.

(The only family headed by a Petitt in the county in 1850 was Samuel, at household #273.)

William M. Fugett’s wife was Hannah Lewis, daughter of Thomas Lewis and Hannah Hopkins, and sister to John P. Lewis Sr., with whom Andrew Jackson Pettit was living in both 1850 (at age 4) and 1860 (at age 15.)

This suggests a relationship between Martha Petitt in this household, and Jackson Petitt in the John Lewis Sr. household. Jackson’s death certificate listed his parents as Thomas Petitt and Sarah Cassity, though. (Well, really it said Thomas Peditt.)