In the 12th century, Robert de Beaumont, third Earl of Leicester, was known as "Blanchmains" or "Wyghtmains", because of his white hands. It is believed that his descendants continued to use this name when the use of surnames became common. This theory seems quite likely, because in later times families with the name "Wyghtman" or "Wightman" were owners of land which had formerly belonged to this earl, in Leicestershire and other nearby counties.

 

    In a very early written record (a 12th century roll describing the holdings of some residents in the County of Suffolk and the parish of Alteston), the name is spelled "Wihtman". During the 14th century, it is found as "Wyghtman", "Whitman", "Whiteman", "Weightman", etc. The spelling varied according to the locality or to the parish priest who was writing the document. It was not unusual to find the same person referred to by many different spellings within a relatively short period of time.

    The change in the spelling and pronunciation of the name is interesting. In America and in England, the words "wight" and "white" are pronounced very similarly, so it is easy to see how the spelling could be interchangeable. On the other hand, "weight" has a quite different pronunciation in those countries. In Australia, however, that word too is pronounced very much like "wight". Perhaps that was the case also in England, at about the time spellings were becoming standardized there.

    Apparently, the spelling of names and words was quite arbitrary until sometime during the 17th or 18th century. Then, families living in different areas settled on different ways to spell their names (perhaps depending on how the parish priest or a local official had most recently spelled it on a document). From a certain time onward, the spelling would remain constant within that local family group, but the pronunciation might change gradually from one locality to another.  

 

References:
  Our Marvelous Native Tongue: Robert Claiborne (1983)
  The Mother Tongue -- English and How It Got That Way: Bill Bryson (1990)