The weeping willow is (not unexpectedly) symbolic of grief; lamentation; mourning; and sorrow.
The weeping-willow has been associated with sorrow and bereavement ever since the Babylonian Captivity when the Jews became captives of Nebuchadnezzar in 597 B.C.
In the Native American culture a willow tree represents an Iroquois grave.
The Willow was a symbol of the Greek Underworld goddesses, mostly notably Persephone. Orpheus carried a willow branch when he went to the Underworld, and helped him get his gift of speech to become a famous poet.
The symbolic tree of human sadness is carried at Masonic funerals