So far I've just found one child of the marriage. From Ancestry.com:
Joanna Hooper
christening: 18 November 1814
AWRE WITH BLAKENEY,GLOUCESTER,ENGLAND
father: William Hooper
mother: Elizabeth
(Another user-submitted entry lists the mother as Elizabeth Cadogan)

Then on the Gloucestershire Archvies database
http://ww3.gloucestershire.gov.uk/genealogy/Search.aspx
there are the following Wills from Awre, which may shed some light on the families around that time:
1835 hooper robert presbury awre 1835/202 yeoman
1816 cadogan charles awre 1816/129 fisherman
1818 cadogan william awre 1818/ 24 yeoman
1826 cadogan joanna awre 1826/110

Plus some earlier ones:
1766 cadogan jonathan awre 1766/ 36
1766 cadogan jonathan awre 1766/160 yeoman
1724 cadogan walter awre 1724/ 83
1724 cadogan walter awre 1724/223 yeoman