This is just a guess, but I just came upon an article about British surnames that are disappearing (https://blog.myheritage.com/2011/04/rare-british-surnames/).
It referenced one name with the “berry” component: Berrycloth (English)
This location name is from the place called ‘Barrowclough’ near Halifax in West Yorkshire. The derivation of the place name is from the Old English pre 7th Century ‘beara’, meaning grove, or wood; and “cloh” (a ravine or steep slope). Locational names were distributed around the country when those who bore the name moved from their original homes and went to live or work in another town or village, becoming known as ‘Berrycloth’.“
Since surnames often became given names that were passed down, I wonder if “Woods” could be the original meaning.
I have many Littleberrys and Greenberrys in my tree; perhaps these originally meant “Littlewood” and “Greenwood”?