Hooper family name was from my husband's side, which I had worked on years ago. I looked through my materials and have the following info for you:
(1) On website https://archive.org, there is a digital book titled: Hooper Genealogy by Charles Henry Pope and Thomas Hooper, published by Charles H. Pope, in Boston, 1908. If you have not seen it, you should check it out. Should also be in Maine State Library?
(2) On ancestry.com, several people have been working on Hooper lines. Some are better documented than others. The documentation should give you places to check out.
(3) In 1850 U.S. Census of South Berwick, a William H. Hooper, age 10, is living with Nathaniel and Hannah Walker. This one is 8 years older than the one you mentioned.
(4) Due to fire in Ellsworth, Hancock County, Maine, many early records were destroyed.
(5) Registry of Deeds in Hancock and Washington Counties, Maine can be useful.
(6) I have a Samuel/William Hooper marrying Mary Leighton in Harrington in 1840. Children: Forrest Albert (for Albert Forrest), Matilda Adelaide (for Adelaide Matilda), Eliza Amanda (or Amanda Eliza) all depending on what record you look at. Also, potential children: William Henry Hooper (source says he left home), Calvin Hooper and James Hooper. I did not continue researching this line.