What does "Just like a willow" mean?

In the song "It's now or never" by Elvis Presley I encountered this line:

Just like a willow

We would cry an ocean

If we lost true love

and sweet devotion

I know "willow" is a kind of tree, but "just like a willow" doesn't seem to be an idiom. Are there any subtle meanings hiding under "just like a willow"?


Solution 1:

I think it refers to a weeping willow:

a type of willow tree that has long, thin branches that hang down.

that suggests the idea of "crying".