Some marine animals, like seals, shed tears to get rid of excess salt. In this theory tears, like hairlessness, bipedalism, and other human oddities, is a response to saltwater living. More to the point, it's not at all clear that human tears do function to get rid of excess salt. Nor does that explain why grief, anger or joy causes tears. Seals shed tears all the time, not just when plucky little kids are orphaned.
Tears have a strong communicative power.
He taught himself to cry again as an adult, and has witnessed rivers of tears in the course of his therapeutic work. Many people cry only when they're alone, when there's no one to communicate with, so if their value is in acting as a signal, they are an involuntary signal. Many theories about emotional tears focus on crying babies, sometimes not bothering to distinguish between the acts of making crying sounds and shedding tears, either of which can happen without the other. Any theory that relates emotional tears to infant crying must deal with two facts. Many infant primates make various crying sounds without shedding tears and are perfectly able to get parental attention.