Hi. I've learned from animal communicators that animals pick up on our stress, and try to take this from us. Therefore, they can develop similar pains to us, etc.
Cats, according to the Dowsing course, like negative energy. According to this course, when they sit or lay on us, they are trying to absorb our negative energy into their fur, and when they're "full," they jump off, shaking or liking it off them. Hopefully this doesn't harm them.
I'm just repeating what I've read and learned. I'm not knowledgeable beyond this. But I did hire an animal communicator before I moved, and it seemed to help tremendously. I've witnessed a communicator in person talking to others' pets, and the results were amazing.