The Norman Conquest of England in 1066 brought many new words to England from which surnames were formed. Stubbs was one of these new Norman names. It was specifically tailored to its first bearer, who was a short or stocky person, having derived from the Old English word stybb, of the same meaning.
A broad and miscellaneous class of surnames, nickname-surnames referred to a characteristic of the first person who used the name. They can describe the bearer's favored style of clothing, appearance, habits, or character.
A multitude of spelling variations characterize Norman surnames. Many variations occurred because Old and Middle English lacked any definite spelling rules. The introduction of Norman French to England also had a pronounced effect, as did the court languages of Latin and French. Therefore, one person was often referred to by several different spellings in a single lifetime. The various spellings include Stubbs, Stubs, Stubbes, Stubb, Stubbe and others.
First found in Staffordshire where they were granted lands at Water-Eaton and Bloxwich by William the Conqueror for their assistance at the  Battle of Hastings in 1066.
There are elaborate accounts of this family's descent from Belmeis or Beaumeis from Beaumeis-Sur-Dive from Calvados in Normandy through Richard Belmeis, the founder of the family, who was a follower of Roger de Montogomery who was Sheriff of Shropshire and later Bishop of London, about 1100.
Many English families left England, to avoid the chaos of their homeland and migrated to the many British colonies abroad. Although the conditions on the ships were extremely cramped, and some travellers arrived diseased, starving, and destitute, once in the colonies, many of the families prospered and made valuable contributions to the cultures of what would become the United States of America and Canada.
Research into the Origins of individual families in North America has revealed records of the immigration of a number of people bearing the name Stubbs or a variant listed above:
John Stubb who settled in Philadelphia, Pennsylvania in 1846;
Mr. Stubbe, his wife and five children settled in Philadelphia, Pennsylvania in 1792;
Daniell and Hontford Stubbs settled in Virginia in 1637
Motto ‘Cedant arma labori’, Translated: ‘Let arms give place to labour’