You may not have been here when I posted about my kitty at mom's house. Got her in 1987, and she was already 6 months old. Who knows how old she will live to be. She is my "old lady" who can't be bothered with the young-uns (i.e. the other two cats at mom's house). When I went to visit her about a month ago, she was all forlorn and neglected looking. She had quit grooming herself, has a clubbed foot that prolly happened while jumping down from a tree and healed badly, and is blind out of one eye. I joke about her name, "B.C." cuz it is such a versatile name for her. Originally, she was named, Black Red Oak Baby Cat. I shortened it to Baby Cat, and then to B.C. It has stood for Beautiful Cat, black cat, baby cat, best cat, bad cat, blind cat, and most recently, bolemic cat. Yes, Bolemic Cat. She is nothing but skin and bones these days either because of her urping up all the time. Anyway, all that said, I went over there a couple-or-three weeks ago and took with me a wire brush, some cat-bath washcloths, and a new toy for her. You wouldn't believe what a difference brushing her made. She is a new cat. She has resumed grooming, she plays with her toy, and looks 100% better. Not sure I can do anything about her urping up all the time. Never heard of a pet having an eating disorder before, but I suppose it happens.
Actually I think a lot of older cats have sensitive tummies. We've had a couple over the years. Cleo actually had trouble with that when I first got her but has been better lately...dunno why. Maybe just the fact that she is on better food and has been less stressed? Dunno!
Get her some Nutri-Cal. It's a malt-flavored paste, mineral oil based, that comes in a tube like toothpaste. You can get it at the pet shops, sometimes it's in the dog section because it's good for both dogs and cats. It's packed with vitamins, minerals, and lots of calories. Hunters use it to give their bird dogs extra energy on a long day in the field. It digests quickly and the mineral oil will ease out any hairballs that might be in the cat. (Are icky grey small tapered solid things coming up in the vomit? Them's hairballs. If she was having trouble grooming that may be part of the problem.)
After she's been on the Nutri-Cal for a couple of weeks, her stomach should be settled enough to stop the vomiting. (I assume she's not vomiting blood or bile or anything nasty like that, just regurgitating partially digested food.)