Leverett was born in 1881 - which means that he wouldn't show up in a census until he was 19. By this time he was already married, which makes it hard to track his parents.
On his death certificate, Leverett's parents are listed as John Franklin Waters and Mary Elizabeth Harding. I've taken this information as true, but have been unable to find a couple matching this description. His mother, Mary, was married a second time to John B. Whitlock. I've been able to trace this step family. I need to send for a death certificate for Mary, who died in 1928.
My mistake was to assume that Leverett's daughter knew her grandparent's names. It appears that she didn't! About a week ago, I applied to receive a copy of his Social Security Card Application (SS-5). I expected that this record would simply confirm his parentage. Boy, was I wrong!
This application appears to have been filled out by Leverett himself. The letters are very carefully and deliberately written, and I notice that he spelled his name with two 'T's in his surname and only one in his first name.
I also notice that he lists his parents as James Balis Watters and Mary Pilgram. What!? Time to start my Wat(t)ers research all over again. I'm really glad that I sent for this document!