In my own experience, both professionally and personally, crying is one of the body's ways to bring itself back to balance. It is not necessarily a sign of weakness or even sadness. Infants cry to communicate with their universe. New mothers cry... a lot. And so do the rest of us.
For many years, on those rare occasions when I cried, I'd get a headache. But when the grief is so intense, the tears wash over and seem to take out all the toxins and pain; at least, that's my non-scientific analysis.