The Collaborative International Dictionary
Weeping tree \Weep"ing tree\
Any tree having pendulous branches.
A tree from which honeydew or other liquid secretions of insects drip in considerable quantities, esp. one infested by the larv[ae] of any species of the genus Ptylus, allied to the cuckoo spits, which in tropical countries secrete large quantities of a watery fluid.
Wikipedia
Weeping trees are characterized by soft, limp twigs. This characterization may lead to a bent crown and pendulous branches that can cascade to the ground. While weepyness occurs in nature, most weeping trees are cultivars. Because of their shape, weeping trees are popular in landscaping; generally they need a lot of space and are solitary so that their effect is more pronounced. There are over a hundred different types of weeping trees. Some trees, such as the cherry, have a variety of weeping cultivars. There are currently around 550 weeping cultivars in 75 different genera, although many have now disappeared from cultivation.
Usage examples of "weeping tree".
Anigel and Immu had approached Tass Town's island with great care, and their boat now lay concealed beneath a weeping tree that grew from a cleft in a great precipice along the western shore.
It saw the Demon standing at the top of one flight of marble stairs, one Tragamor halfway down another flight, and the other brooding on the lower terrace beside a weeping tree.
Although large urns had been planted with some sort of weeping tree to soften the harsh architecture, the effect was forbidding, rather than welcoming.