Helen: You gave me very little to go on as William Hoopers are very plentiful in Mass.
I have a Hooper Genealogy book with the first 87 pages on the Reading, Mass. Hoopers.
There are many references to Williams in those 87 pages. This book is Hooper Genealogy compiled by Charles Henry Pope and Thomas Hooper and published in Boston, Mass in 1908. Should you wish to contact me again, my e-mail address is JacknOmie@aol.com