The DAWES is usually found with the following variations DAWS and DAW. It is less frequently found as DAWE although there is a large number of these families found in Newfoundland, Canada.
There are a number of different explanations for the surname's origin:
1) From a biblical perspective it is supposed to mean the Son of David. This is the explanation usually given in the generic genealogy books on various family names.
2) Another concept is named after the Jackdaw bird. There are numerous pubs named after this bird such as "The Three Daws" in Kent and it could indicate that a DAWES family lived in the vicinity of these birds. See Wikipedia
3) There is a third variation that could be associated with a physical location and I think that this might make the most sense. The name could have started in Normandy and been brought over with William The Conqueror and have been spelled as a D'awes meaning near or by something. This last variation needs a lot more research.