Stephen and Lydia Weaver Arnold, of Warwick, RI, may have been aware of a troubled fifteen-year old by the name of Benedict Arnold in Norwich, CT, when they gave their newborn son the same name but, if they were related (as is claimed in the attached image), no evidence is found in a cursory search of the two families.
Benedict the Infamous was born to Benedict Sr. and Hannah Waterman King Arnold 14 Jan. 1741. The "other" Benedict was born to Stephen and Lydia Weaver Arnold on 14 Mar. 1756. The letter claims that Stephen was the half-brother of Benedict the Infamous but, since Benedict Sr. and Hannah were married at a fairly young age (age 18 and 25 respectively) and died within 2 years of each other, this claim seems unsubstantiated on the fathers' sides. Hannah Waterman was the young widow of Absalom King and they had a child, but it was a daughter, Hannah King. Hannah would have been the only half-sibling to Benedict the Infamous, and she died in 1739. Of course, the web site giving this information (www.hdhdata.org/roots) says in one place that Absalom died at sea in 1723, and Hannah Waterman is supposed to have married him in 1730, with young Hannah being born in 1731, but the date of death may be a typing error (perhaps he really died in 1732).
Genealogical records (familysearch.org) show that Stephen's father was Phillip Arnold, and that branch of the Arnold family was in Rhode Island four generations prior to the birth of the "other" Benedict. The immigrant ancestor, another Stephen, was born in Somersetshire, England in 1622.
Benedict Sr., the father of the infamous Benedict, was born in London, England in 1715 and was the immigrant ancestor.
Benedict the Infamous enlisted in the Connecticut militia in 1757 to fight against the French invasion from Canada. Although he never saw action, it made a quiet civilian life pretty boring. His mother died in 1759 and his father in 1761. He served for several years as an apprentice to his mother's brothers, Daniel and Joshua Lathrop, who were apothecaries. In 1761 he went to London to purchase items for his own shop. Always spending more than he had, he followed one "money-making" scheme after another, always looking for adventure. His life and marriages from this point are well documented.
The "other" Benedict enlisted in May 1775 and served as a private off and on as needed for a total of "more than seven months". He married Elizabeth Andrews in 1793 and lived, apparently, a quiet and exemplary life. He died in 1829, and his widow Elizabeth died after 1838. His life would have been unnoticeable except for his unfortunate name!