What kind of test did the vet run? If it was the Elisa test (sometimes called the stick test), that test does not conclusively prove that a cat has FeLV. If all your vet did was draw a little blood and drop it into a plastic device with dots on it, that is the Elisa test.
When a cat is exposed to FeLV, their body will try to fight off the virus. During that time, they will show positive on an Elisa test. Many cats are very sick at this time as they are fighting a virus in their system. But if your cat was vaccinated against it, about 90% of the cats will ultimately fight off the virus. If unvaccinated, the odds go down (I believe) to about 50%.
If the cat cannot fight off the virus, then the full disease enters their blood stream. The only test the positively confirms full blown FeLV disease is called the IFA test. The test requires a vial of blood and most vets don't have the lab to run the test so they send it off to a lab.
So Elisa indicates exposure, IFA indicates full blown FeLV. You might want to call your vet and confirm what test he ran and before you make any decisions about him, ask for the IFA test. My last vet had never run one before and many vets (unfortunately) diagnose the disease after the Elisa test.
Verify with your vet about changing foods for him right now. In my house, I will give my cats a high quality food that they like that will encourage them to eat. If he truly has the disease and is that far along, he will become lethargic and he won't want to eat. He might get very clingy to you and will want to be held and cuddled as much as possible. I have discovered over the years that they will tell you when they have had enough, and one major sign is when they simply refuse to eat. Some otherwise social cats will find a dark quiet place to hide in. Every cat is different and there aren't any clear answers for you.
If it hasn't been run already, please ask for the IFA test to prove this one way or the other. And let us know how things are going, OK?