Following Martin's comments, (I'm sure he means 1780), Cornwall Parish Clerks do list two marriages for George Eddy - one to Catherine Richards and one to Catherine Edwards - both on October 4, 1780 and both in Sithney, Cornwall. The marriage to Catherine Edwards has 2 witnesses - Robert Edwards and William Pascoe. Like Martin, I would go for Catherine Edwards.
There are no apparent records (baptism or marriage) for any Mathew Eddy or Elizabeth George in Cornwall around that time.
George Eddy was baptised February 11, 1757 (in Breage, Cornwall) and was the son of George and Elizabeth. This may have caused the confusion with your Elizabeth George name.
William Eddy's baptism is listed as June 1, 1781 in Sithney and shows his parents as George and Catharine (note spelling). Also William's marriage May 18, 1812 in Sithney to Elizabeth Polmer (also note spelling).
Happy hunting!