Via Barker, a pointer to a theory from evolutionary psychology that tears are a true signal that the person crying is vulnerable and in need.
Emotional tears are more likely, however, to function as handicaps. By blurring vision, they handicap aggressive or defensive actions, and may function as reliable signals of appeasement, need or attachment.
Usually you should be skeptical that signaling is evolutionarily stable. For example if tears convince another that you are defenseless then there is an evolutionary incentive to manipulate the signal. Convince someone you are defenseless and then take advantage of them.
A typical exception is when the signal is primarily directed toward a family member. Family members have common interests because they share genes. Less incentive to manipulate the signal means that the signal has a better chance of being stable. And babies of course have few other ways of communicating needs.
Of course children eventually do start manipulating the signal. They learn before their parents do that they are becoming self-sufficient but they still have an incentive to free-ride on the parents’ care. Fake tears appear. But this is a temporary phase until the parents figure it out. Not surprisingly, once the child reaches adulthood, crying mostly stops: Nature takes away a still-costly but now-useless signal.