Googling the surname seems to indicate that it's French, derived from a town in the North of the country.
http://en.wikipedia.org/wiki/Douay
http://en.wikipedia.org/wiki/Douai
http://en.geneanet.org/search/?name...ubregion=F80®ion=PIC&country=FRA&bdd=g3_arbre
http://www.etymonline.com/index.php?search=rheims-douay+version
http://search.ancestry.com/cgi-bin/...new=1&so=3&MSAV=0&msT=1&gss=feeder&gsln=Douay
Surnamedb also says that the surname was sometimes anglicized to Dewey, and that Douay or Douai is derived from the old Gaulish name, "Dous". It's also implied that it was specifically a Norman French surname, which might explain things if it occurs in Ireland or Britain.
http://www.surnamedb.com/Surname/Dewey
Hope I helped.
The distribution is very concentrated around Somme. The variant that matches the village is less common and more closely tied to the village it comes from.