My 15 year old, neutered, boy cat has been vomiting bile for several months now. He is sick at least once a day. He has been to the vet on several occasions and nothing was found until Saturday when she says that there is a thickening, high up near his stomach. I don't know what to do. He never vomits food and is still eating although he is losing weight. He has lost about 1.5k, and now weighs 5k. She said we can do scans and even a biopsy but if it was a tumour, there would be little that they could do. Any suggestions?

No doubt Ernie has given many joys in those 15 years.
But it sounds as if you may be at a point that you need to asses his quality of life.
By "thickening" I am assuming that that the vet felt something abnormal internally, not under the skin, Is this correct?
And by scan do you mean X-ray, ultrasound, MRI?
If not already done I would at least do an X-ray in order to see if what he/she is feeling is visible on film.
I am one of those people who needs an answer before I make choices, even if that answer is not a favorable one.
I'm certainly not implying that you haven't sought an answer, do you recall what testing has already been done?
I'm also gathering that your vet feels that either 1) Ernie's chance of surviving anesthesia and surgery are not good because of his general health at this point or 2) that the thickening that he/she feels is involving internal organs.
That's only my summation from what you have written, I may be wrong about the reasons.
Suggestions? I really don't know that I have any except that if I were able to do so, I would gather every bit of insight that I could about why he is eating, losing weight, and continuing to throw up bile and make an informed decision from that information.
Some of that information no doubt you already have.
I realize testing and trying to find that answer can be rather expensive and frustrating to say the least.

Best wishes to you and Ernie