They are closely related, and both cleanse the body of toxins, but crying makes people turn inwards, while laughter releases them.

Link: Tears of Joy and Tears of Sorrow: The Similarities and Differences Between Laughter and Crying [theunboundedspirit.com] via @sofoarchon

"Do you think high mirth and low sadness are closer to each other than regular affect?"

I think all affects vary by intensity only. How forcefully it is felt, In so far as our behavior is based on pursuit of pleasure (aka Happiness) then yes, they are close.
I think the pleasures and the pain we feel motivate us to pursue or not. We are unique in our aware ness of our own feelings, our ability to share our joys and pains in a shared language with shared grammar, and meanings.