To go into mourning, especially for a sweetheart or bride. Fuller says, “The willow is a sad tree, whereof such as have lost their love make their mourning garlands.” The psalmist tells us that the Jews in captivity “hanged their harps upon the willows” in sign of mourning. (cxxxvii.)
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894