
Some people cry without tears because of a genetic disorder that results in lacking the ability to produce tears (alacrima).
Crocodile tears (or superficial sympathy) are a false or insincere display of emotion such as a hypocrite crying fake tears of grief. The expression comes from an ancient anecdote that crocodiles weep in order to lure their prey, or that they cry for the victims they are eating.
Why we Cry or weep?
Crying is increased lacrimation due to strong emotional stress, suffering, mourning, or physical pain. This practice is not restricted to negative emotions; many people cry when extremely happy.

regeneration subsequent to Bell's palsy or other damage to the facial
nerve in which efferent fibers from the superior salivary nucleus become
improperly connected to nerve axons projecting to the lacrimal glands
(tear ducts), causing one to shed tears (lacrimate) during salivation
while smelling foods or eating. Presumably, one would also salivate while crying due to the inverse improper connection of the lacrimal nucleus to the salivary glands, but this would be less noticeable.