I've found two Averys and both were male, I don't know why I thought it was a girl's name!
The two I've found were son of Hungerford and the first Elizabeh and the son of his brother Lancelot and his wife Mary nee Hatt. (from familysearch).
The children I have found for Hungerford and Elizabeth Hunter are
i. LEVI WHITFIELD, b. Bef. 22 Aug 1790, Stanford in the Vale.
ii. AVERY WHITFIELD, b. Bef. 10 Jun 1792.
iii. WILLIAM WHITFIELD, b. Bef. 11 Nov 1793 presumably died before 1798
iv. ELIZABETH WHITFIELD, b. Bef. 22 Feb 1795.
v. ANN WHITFIELD, b. Bef. 16 Oct 1796, Stanford in the Vale; d. Bef. 07 Dec 1801.
vi. WILLIAM WHITFIELD, b. Bef. 01 Jul 1798, West Challow.
vii. JOSEPH WHITFIELD, b. Bef. 20 Oct 1799, West Challow.
Hungerford and Esther had one child
viii. ANN WHITFIELD, b. Bef. 27 Aug 1803, Stanford in the Vale; d. Bef. 30 Oct 1803
and with Elizabeth Painter
ix. ROBERT WHITFIELD, b. Bef. 19 Feb 1805.
x. ANNE WHITFIELD, b. Bef. 31 Jul 1814.
Levi, William and Joseph appear on 1841 and later censuses in the Stanford itv area.
Avery is in Cricklade in 1841 with wife and 3 children, one son called Hungerford.
Robert might be the one buried on 6 Mar 1851 in Wantage, but I can't find him in 1841.
Ann and Elizabeth may have married, so would be more difficult to track down on censuses unless they died before 1841.