In "Mary on the Wild Moor," the final verse is,

The father did soon pass away
And the child to the grave was soon borne
And no one lives their to this day
And the cottage to ruins has gone.
The villagers point to the spot
Where a willow droops over the door
Saying there Mary perished, alas,
From the wind that blows o'er the wild moor.

I've always taken willows to be a symbol of grief or mourning in folklore, presumably because they droop and "weep."