Just refer to it as a weeping willow, or willow tree. I’ve never seen or heard “weeper” as a name for these trees and was very confused upon my initial reading. I didn’t know if Roberts was referring to the widow’s walk, or a part of a house with which I am unfamiliar. House have branches, too.
Using the name of the actual tree wouldn’t have pulled me so far out of the story that I would write such a long note about my confusion!