Weeping tree \Weep"ing tree\
   (a) Any tree having pendulous branches.
   (b) A tree from which honeydew or other liquid secretions of insects drip in considerable quantities, esp. one infested by the larvae of any species of the genus Ptylus, allied to the cuckoo spits, which in tropical countries secrete large quantities of a watery fluid. [Webster 1913 Suppl.]

Source: The Collaborative International Dictionary of English v.0.48
 

Weeping tree \Weep"ing tree\
   (a) Any tree having pendulous branches.
   (b) 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.

Source: Webster's Revised Unabridged Dictionary (1913)