Dogs can vomit or regurgitate and they are NOT the same thing. So which is your dog doing? You do not indicate if you clearly understand the difference.... when using the TERMS. If the dog is regurgitating food (just eaten) with little to NO heaving; the most likely cause is mega-esophagus. It can be acquired later in life. (I have had two male dogs to have it.)
I see you now "claim" in a comment you just paid 4K to do testing on the dog (including an MRI and blood work). That is actually important and you LEFT THAT OUT - which is NOT HELPFUL!
You also LEFT out the results of said blood work, including calcium levels (which can be OFF - if the dog has CANCER). Cancer is a 50% possibility; in all dogs over age 10 and one of the major signs of advanced cancer is sudden & unexplained weight loss. You seem sure, the lack of enough CALORIES - is the ONLY cause for the weight loss, even though you mention the dog re-ingesting the regurgitation. (????) Do you want to clarify any of that, for those of us who still - don't read minds?
If you only feed the dog once a day, it may (now) be suffering low blood sugar due to only getting one meal (which can cause nausea) so make sure you feed 2-3 times the total calories fed, in a day.
If you see whole & undigested food come immediately BACK UP (that suggests mega-esophagus) & is more commonly seen in older dogs. It is treatable. No, it does not show up on the testing you claim was done.
It would really help to have more details; as you have left major things out of your post, that would be helpful to know. But instead, you LASH OUT at us, as though we can READ MINDS about the unpublished information (you SEEM to think -we should somehow MAGICALLY & automatically KNOW) despite nothing said - in your Original Post.
I would second the advice - to get another opinion from another vet, if you have no firm diagnosis. The dog is NOT vomiting & loosing weight WITHOUT a MEDICAL REASON (you are right on THAT). "Old age" is NOT a cause OR diagnosis. (That is a cop-out; and the sign of an UNCARING, or possibly stupid or lazy vet.) Any caring vet would be very CURIOUS & CONCERNED -(esp after charging you 4K, for essentially nothing).
For now, you can go on the theory of mega-esophagus and RAISE the food bowl (put it on a stool or bucket -so the neck will be level or higher -when the dog eats. Change the food to canned, or make any kibble into a soft watery gruel and/or try feeding the dog the soup mentioned in Amber's post. Pureed meat or Gerber meat baby food can be added.