The geography suggests there is a link but the names I have are not in the list on the site to which you have given a link...
John WESTON m Rhoda BINDLEY (or BINGLEY) 29 Sep 1778 Wigston Magna, Leicester, [IGI-submn7813235]
1] dtr:
Rhoda WESTON b 1778-9 Arnesby, Leics
1.1] g-dtr:
Martha WESTON b 4 Jun 1803, bap 8 Jun 1803 St Margaret, Leicester [C034613]
Martha WESTON, o. t. P. of St Mary, Nott'ham, m 27 Nov 1826 St Nicholas, Leicester George BENNETT (o.t.P.) [personal 8113910; PR#392]
witnesses: Thomas BENNETT (signed) & Susannah BENNETT (signed)
2] son: Edward WESTON bap 20 May 1782 Arnesby, Leicester [C034331]
Edward WESTON† m Fanny VALENTINE 2 Mar 1819 St Margaret, Leicester, [M034611]
†
http://www.leicester.gov.uk/about-leicester/lordmayorcivic/roll-of-mayors/1800-1899-roll-of-mayors/1840-1849-mayors/1845-edward-westonI have put the names I have deduced to be my direct ancestors into bold.
Rhoda appears to be the sister of the erstwhile mayor of Leicester (based on 1851 census), by which route I have deduced the parents.
There are a couple of Wigston Magna IGI baptisms (Matthew 17 Apr 1783, and Mark 10 Mar 1785) which might fit into the family, but about which I'm rather doubtful.
Christine