I think it has to do with the body movements.
When you laugh your body opens up, it relaxes (I can't imagine anyone relaxing and letting go in a cringed position). This is one of the reason why laughter feels so good - it relaxes you, relieves tension. You can't be tense and laugh out loud at the same time. Unless you laugh a bit while taking cover (but then again it is a small controlled laugh, when you can't enjoy it to the fullest).
Crying is the opposite - let me open up, invite the world, breathe with the full chest... and cry... impossible. Your crying will stop right there. That's why they tell you to breathe in order to take the focus away from crying. Also there is a little trick - when you feel like tearing up to cry in public, when you shouldn't, (for example, during public speaking - roll your eyes to the ceiling... I tried, it works).
So, yes, when you cry the body gets in the protective position - imagine a hedgehog - to protect himself he rolls into a prickly ball. We also tend to stay away from public when we cry (the same privacy we need when we go about "our business". Animals like that privacy as well.)
And, so, my fellow Laughing and Crying companions, ask not what science can do for you, ask what you can do for science!
By the way, that was my own version of a pseudo-scientific concoction