Why do we weep? And why don’t most other mammals?
Problem the first: There’s no reason for Nature to have designed us (by way of evolution) to use leaky eyes or a heaving chest simply to “process” any of our emotions. In fact, as a general rule, emotions aren’t the kind of thing that need to be “processed” at all — as if they were industrial byproducts that needed to be discharged from the thinking factory. Emotions (and their expressions) aren’t mere side-effects of something else — they’re purposeful unto themselves. They evolved because they put our brains and bodies (technically, those of our ancestors) into a locally-optimal state for dealing with specific problems or circumstances. If evolution devised to make our bodies do something, then the action is unlikely to be a meaningless side effect. There has to be a point to it.