There are 37 listings in the Social Security Death Index (SSDI) for individuals with the surname Reaid and nearly 200 in US Census records for various years and locations, which certainly validates the spelling in relatively modern times. Of course that doesn't answer the question of whether the original ancestor might have misspelled it. It's logical to assume, but not definitive, that it's a variation of Reid, generally held to be Scottish. Also Read, Reade, Reed, Red, Redd and perhaps others.
Reid itself is a surname of some controversy. See: http://www.surnamedb.com/Surname/Reid