Willie drowns in the (Yarrow). (Details of how and why vary greatly). His lover dreams a dream of woe. She sets out and finds Willie's body, and uses her hair to pull him from the water. In many accounts she (promises to) die for sorrow
Several scholars, among them Norman Cazden, have claimed that this song is the same as Child 214, "The Dowie Dens o Yarrow/The Braes o Yarrow." Certainly there has been exchange of verses. However, I (following Leach), would maintain that there is a difference: "The Dowie Dens" is about opposition to a marriage; "Willie Drowned" is about the loss of a love.
A brief summary of the whole discussion is found in Coffin's notes in Flanders-Ancient3. It's not clear what he believes, except that the two songs are a mess and quite mixed. Which can hardly be denied.
Palgrave's _Golden Treasury_ includes a piece (item CLXIII) titled "The Braes of Yarrow," credited to J. Logan, which is clearly built upon this theme -- but it looks like a literary rewrite. Palgrave's next item (CLXIV), "Willy Drowned in Yarrow," is the real thing, though probably somewhat touched up by his (unnamed) source.
Child lists "Annan Water" as an appendix to this ballad, though it appears to me that, if it's related to any of the Child ballads, it's #216, "The Mother's Malison, or, Clyde's Water." - RBW