We have a senior cat, around the same age, that has similar problems. His problems started with a diagnosis of high thyroid, which led to us putting him on a low iodine diet. The vet mentioned that it was likely that two other things would happen as well: there would probably be problems with his kidneys, and also that it was likely that he was going to have issues with acid reflux.
The latter issue has been the major concern. After about six months on the low iodine diet, the reflux started to kick in. We started by putting him on rantidine (zantac) -- if I recall it started out with about a third of a pill or so, ground up, and added to something with really strong flavor that he would gulp down (we used things like the cheap canned fish, or "potted meat" from walmart). When he was really bad off, I'd grind up about half of an antacid pill and half a zantac together, and force feed him with a dropper. When it kicked in, he'd eat like crazy and gain the weight back.
If it's the same thing, I should note that it's progressive and/or the medicine loses its effectiveness. We're now up to half a pill of Prevacid (generic capsules, cut open to release the little "time release granules) a day. It's also getting progressively harder to trick him into eating it. It's also been a serious challenge to stay in front of this problem.
We've gotten another year out of our awesome cat, but I'm not sure there's much more left. Overall, he's still happy at this point, but it's getting closer to the end.
If it is acid reflux, you can probably tell by the smell when he vomits. If the reflux is bad, it will have a serious vinegar smell.