Esther Connelly was most likely James Connelly's daughter. Her descendants are genetically related to those of Rebecca Mira Connelly, who married Joshua Gibbs. Rebecca was not the daughter of William Connelly and Rebecca Sherrill. That Rebecca Mira Connelly married Archibald Kincaid. The only other Connelly who could have been Rebecca's father was James.

Esther Connelly married David Ballew on May 2, 1817 in Burke County, North Carolina. They had 16 children together. All of their children were born in North Carolina, except for the youngest, Martha Elizabeth, who was born in Georgia. They moved to Gilmer County, Georgia by 1850.

1820 Census: Burke County, North Carolina

1830 Census: Burke County, North Carolina

1840 Census: Macon County, North Carolina

1850 Census: Subdivision 33, Gilmer County, Georgia -
David Ballew, age 61, b. North Carolina
Easther Ballew, age 53, b. North Carolina
Alfred, age 22, b. North Carolina
James, age 21, b. North Carolina
Jason, age 19, b. North Carolina
Jackson (Caleb Jackson), age 17, b. North Carolina
Samuel, age 16, b. North Carolina
Archibald, age 15, b. North Carolina
Addison, age 13, b. North Carolina
Mahala, age 14, b. North Carolina
Martha E., age 6, b. Georgia
Susan Liles (Stiles), age 23, b. North Carolina
Samuel P., age 4, b. Georgia
Americus, age 2, b. Georgia
Mary, age 6/12, b. Georgia

This census was taken on Oct, 25, 1850 and Susan and her children were counted a second time here. The first time was with her husband Benjamin H. Stiles in Cherokee County, North Carolina on Jun. 1, 1850.

1860 Census: Catoosa County, Georgia -
D. Ballew (David), age 71, b. North Carolina
E. (Esther), age 64, b. North Carolina
Jas. (James), age 31, b. North Carolina
Saml. (Samuel), age 26, b. North Carolina
T. M.? Thos. (Thomas), age 20, b. North Carolina
M. C. (Martha E.), age 16, b. Georgia

I'm not exactly sure who Thomas Ballew is. I'm assuming he's one of their sons, but he could also be a nephew or cousin of David's. He wasn't on the 1850 census with David and Esther, unless his name was Addison. I can't find anything further on Addison Ballew. His age on the 1860 census is 20 but this could be wrong. He could be younger or older, but he still should have been on the 1850 census. There is a black smudge covering up something on the census record in front of Thomas' name. It looks like initials, but I can't quite make it out.

Households below David and Esther Ballew in 1860:
C. J. (Caleb Jackson) Ballew, age 27, b. North Carolina
C. (Thursy Caroline), age 23, b. Georgia
M. (Martha R.), age 3, b. Georgia

J. C. (John Columbus) Ballew, age 34, b. North Carolina
M. A. (Mary Ann), age 32, b. North Carolina
G. W. (George Washington), age 15, b. Georgia
J. (Jason), age 8, b. Georgia

A. (Archibald) Ballew, age 24, b. North Carolina
M. A. (Mira A.), age 21, b. North Carolina

1870 Census: Fairplay, Fannin County, Georgia -
Ballew, David, age 80, b. Georgia
Esther, age 74, b. North Carolina
Archabel (Archibald), age 34, b. North Carolina
Ballew, Mary, age 8, b. Georgia
Esther, age 1, b. Georgia

The household below David and Esther is their son Leander and his wife Lucinda. I think Leander may actually be a nephew, and not their son.
Ballew, Leander, age 55, b. North Carolina
Lucinda, age 58, b. North Carolina

David died sometime after Jun. 13, 1870 in Fannin County, Georgia.

1880 Census: Hot House, Cherokee County, North Carolina -
Ballew, James, age 51, b. North Carolina
Nancy P., age 41, b. Georgia
Cinthia A., age 13, b. Georgia
James H., age 12, b. Georgia
Tennessee, age 10, b. Georgia
Julia, age 8, b. Georgia
Brownlow, age 6, b. Georgia
Alonzo, age 4, b. Georgia
Cordelia, age 1, b. Georgia
Esther, age 85, b. North Carolina

Esther died sometime after Jun. 11, 1880 in Cherokee County, North Carolina.

David and Esther had the following children:

1. 1. L. J. Ballew, b. abt. 1819, d. bef. 1848. He married Elizabeth Justice. After his death, Elizabeth married Bryant Gibbs in 1848. L. J.'s first name might have been Leonard.
Leander W. Ballew was not the same person who married Elizabeth Justice.

2. David McKendrick Ballew, b. Apr. 10, 1818, d. Jul. 24, 1894. He married Margaret Jane Higdon on Sept. 29, 1843 in Macon County, North Carolina.

3. Sarah Matilda Ballew, b. May 6, 1820, d. Apr. 28, 1885. She married David Carpenter on May 29, 1839 in Macon County, North Carolina.

4. John Columbus Ballew, b. abt. 1824, d. bef. 1880. He married Mary Ann Connelly.

5. William Connelly Ballew, b. May 25, 1826, d. Feb. 22, 1916. He married Nancy A. Withrow.

6. Susan Ballew, b. abt. 1827, d. aft. 1900. She married Benjamin H. Stiles, Jr. on Apr. 21, 1841 in Macon County, North Carolina. She was also married to Samuel Welchel sometime after 1870 and widowed before 1900.

7. Alfred Collins Ballew, b. abt 1828, d. aft. 1870. He married Mary Ann Ballew on Oct. 24, 1854 in Fannin County, Georgia.

8. James Ballew, b. Aug. 20, 1829, d. Jun. 4, 1888. He married Nancy Parlina Douglass on Oct. 11, 1860 in Catoosa County, Georgia.

9. Jason S. Ballew, b. abt. 1831, d. aft. 1880. He married Rosetta C. Fain on Jun 29, 1856 in Fannin County, Georgia.

10. Caleb Jackson Ballew, b. May 23, 1833, d. Jan. 20, 1922. He married Thursy Caroline Connelly.

11. Samuel Logan Ballew, b. Mar. 1834, d. Sept. 4, 1885. He married Carolina Anna "Annie" Freeland.

12. Archibald Ballew, b. Feb. 11, 1836 , d. Jun. 3, 1918. He married Mira A. Green on Mar. 1, 1860 in Catoosa County, Georgia. She died before 1870. Then he married Arrenia W. Morrow. She died in 1896. Later that year he married Eliza Melvina (Maiden name unknown) Hampton on Sept. 20, 1896 in Union County, Georgia.

13. Mahala Rebecca Ballew, b. Jan. 7, 1837, d. Mar. 22, 1867. She married John Roberts Phillips on Aug. 23, 1855 in Fannin County, Georgia.

14. Addison Ballew, b. abt. 1838, d. unknown.

15. Thomas Ballew, b. abt. 1840, d. aft. 1880. He married Sarah Jane Bell.

16. Martha Elizabeth Ballew, b. Mar. 1844, d. May 17, 1919. She married Thomas Clingman Mull, Sr. on Jun. 5, 1864 in Fannin County, Georgia.