Yep, whenever I cry or seem unwell/lethargic/not myself, my cat responds. I've been in hysterics a lot recently and she comes and pins me down, which tends to calm me down. I notice that she spends more time in my room, especially sleeping, after periods of illness.
She responds to my mom's emotions too.
I also have a large cat of similar weight to the one that's being discussed (diff cat, he's less hands-on), and he doesn't seem to be really overweight, the vet seems to agree? He eats a LOT, so I was really concerned about this - I don't want to deprive him of pleasures (especially not in his senior years), but I didn't want him to get like animals I've known where they did genuinely suffer from their weight (respiratory discomfort or w/e). Turns out it's normal for Maine Coons to eat as gluttonously as he does, especially of meat.