Hi.
Seems both Sarah Hammond and Sarah Roberts very popular name in North (and South) Carolina, and then in Indiana.

1. Using a reference source that has all 1830 FPOC heads of households in the US, FPOC Hammond and Hammonds in various states including MD, NY, PA OH

For NC, taking just the Hammond (although Hammond/Hammonds/Hammon found not far from one another), only these:

a) Levi Hammond, Edgecomb County, NC, District 15, 36-55, 2 FPOC
b) Mark Hammond, Orange County, NC, 36-55, 4 FPOC

3. On the Willis Roberts line: in 1830, two FPOC Willis Roberts in the country:
a. Northampton County, NC, head, 24-36, 4 FPOC in hse
b. Indiana, Rush County, 1830: head, 36-55, 10 FPOC in hsehld. Other FPOC Roberts in county: James, 36-55; Anthony, 24-36, 7 FPOC; Elijah, 24-36, 8 FPOC.

WILLIS ROBERTS: seems useful to go backwards

4 In 1790 census all that come up in search, all white.

i. Willis, Chowan, NC, 5 slaves, no FPOC; same page William Roberts, Esq, 21 slaves; Charles, 13; Thomas, 0; James Esq, 26. All white.

ii. Willis, Granville, NC, image not available

iii. Willis ROBERTSON, Claremont, SC

5. 1800:

i. WILLIS ROBERTSON, Suffolk NY, with 'soundex

ii.Willis Roberts,living in Hillsborough, Person, NC, 9 slaves. Other Roberts, more slaves, same page

6. 1810: 5 Willis Roberts in US, 2 living in Person, NC; 1 in Perquimans, NC; 1 in Northampton, NC; 1 in Isle of Wight VA.

i. Northampton: Jonathan, James, Richard, Claxton, Elias,WILLIS, William,Kinchin. Someone out there who knows NC census style might need to interpret the figures here, it looks like these are FPOC, but I am getting lost in all the columns, for looms, people, etc. On Ancestry, its Roberts, Willis. Not Stated, Northampton, North Carolina, 1810, Roll 42, 743, 140.00
ii. Other Willis Roberts, seem to be white, have slaves, among other Roberts, more slaves.

ii. Didn't check Isle of Wight

7. 1820: five Willis Roberts: One in Northampton, NC; one in Orange, NC; 1 in Capt James Wrights District, Columbia GA; 1 in Shelby KY, 1 in Pendleton SC, 1 in Sumter SC (Robertson).
i. Northampton, Willis seems to be FPOC, with 3 in hsehld; Seem to be a group of Roberts FPOC: Anthony, Claxton, Watson, Mary, Dicks (Dirks?), James. Rachel, Ranson (Ransom?), James Jr, Henry, Elijah. The census is alphabetical, and all Roberts on that page are FPOC.

ii. Orange, NC, seems to be white, have 1 FPOC and 2 slaves.

8. 1830, as above, regarding FPOC, with added note that 15 total Willis Roberts in 1830 census: Lowndes ALA, Mobile, Pickens, St. Clair, all ALA; Elbert, Greene, Warren GA; Clark, Daviess, Owen all KY; Perquimans, Wake, Orange, NY (using 'soundex' getting some Robertson).

8. HAMMOND: The earliest white Hammond in NC, 1790 census, are in Beaufort, Craven, Cumberland, Fayette, Franklin, Granville, Johnston, Lincoln, Mecklenburg, Onslow, Orange, Robeson, Sampson

9. The oldest NC-born black/mulatto Hammond/Hammonds in the 1850 census are:
a. Anna, Fayetteville, Cumberland, NC, 1785 NC
b. David, Division 4, Darlington SC 1800 NC
c. Susan, Division 4, Darlington SC, 1795 NC
d. Dicey, Fayetteville, Cumberland, NC, 1795 NC
e. Wm B. Buncobe NC, 1796 SC
f. Theophilus, 1792, and below-->

Theophilus, 58, (1792)laborer, b. NC; in the Westley Evans hsehld, mulatto, laborer, 41, b. NC, Arrina E. 29, M, NC; Alex, 7, OH, M; Terisa J or P, 5, M, OH; Sarah A, 3, OH; Delila Hammond, 19, NC, Harriet E.P. Evans, 4 mths, OH. All in Oxford, Butler, Ohio

In the 1830 census, Theophilus HammondS is 36-55, 10 FPOC in hse, living in Orange County, NC. So, is 38 years old here.

Does not seem to be in pre-1830 censuses: but 1850 census has two such individuals: one noted above in Ohio; the other age 60, born about 1790 in NC, mulatto, living in Center, Union, IND. Nancy, 41, SOUTH C; Thomas 20, TENN; Jonathan, 17, IND; Jefferson, 15, IND; Lydiann 12 IND; Amanda, 10 IND, older males laborers, seem to have white neighbors.

1880, Theopilus HINNANT, b. 1878 NC, Selma Johnston NC, parents Theo and Patsey.

1900: Theopilus Hammond, b. 1845 MD, father in law to household in HIllsborot, Caroline, Maryland

1910: Theopilus Hammond, b. 1850 MD, Denton Caroline MD

1920: Theopilus G. Hammond, b. 1842, OH, WHITE, Elizabethtown, Bartholomew IND

Perhaps above useul, and hopeful