In looking up "Arms" at surnamedb.com they did not have anything, however, in looking up "Armes," surnamedb had this:
This interesting surname is a patronymic (son of) Armin, from the Middle English, Old French given name "Armin, Ermin", derived from the Germanic element Ermin. This seem to have been the name (of unknown etymology) of an ancient Germanic God, but in later times it was also used in various compound names with the meaning whole, entire. The surname shows the regular Middle English, Old French change of "er" to "ar". One Ermyn Donetoun is recorded in the 1327 Subsidy Rolls of Cambridgeshire, and a Thomas Armyn in the 1481 Register of the Freemen of the City of York. The name is well recorded in Norfolk from the late 16th Century on (see below): Elizabeth, daughter of Henry Armes, was christened on August 9th 1584, at St. James', Pockthorpe, Norwich, and Thomas Armes was christened on October 17th 1588, in the same place. A Coat of Arms granted to the family is a gold shield on a bend blue three hands clenched and couped at the wrist of the first. In Heraldry gold denotes Generosity, and blue Loyalty and Truth. The first recorded spelling of the family name is shown to be that of Katherine Armes, which was dated May 29th 1580, marriage to Thomas Stratton, at Great Massingham, Norwich, Norfolk, during the reign of Queen Elizabeth 1, known as "Good Queen Bess", 1558 - 1603. Surnames became necessary when governments introduced personal taxation. In England this was known as Poll Tax. Throughout the centuries, surnames in every country have continued to "develop" often leading to astonishing variants of the original spelling.