I have recently been following the Eite family and have been in contact with Graham Eite who has successfully documented most of the Notingham / Leicester / Lincoln shires Eites.
My connection is with the Birmingham Eites. Your Edward is also a relative great grandparent of mine, my maternal grandmother was an Eite. Edward's oldest child, Ann Eite, born around December 1820, christened 31st December 1820 at Colstan Bassett, had an illegitimate son, Edward, and went to Smethwick near to Birmingham to give birth. She kept the name Eite for her children. This resulted in the group of Eites now to be found in the Birmingham area, many to be found around Aston, Bordesley and Small Heath districts of the city. Before that time they were mostly in and around the towns and villages of Colston Bassett.
Graham's research goes back as far asjames Eite, 1674, in Radcliffe Nottingham.