I'm really sorry about your kitty.
Ascites (fluid in the abdomen) can be infectious or not infectious. I'm not too sure about cats, but in humans its often caused by liver failure (you'll also see prolonged bleeding, yellowing of the white of the eyes/skin over time). Its true that when you drain the ascites it just comes back (and in the mean time it makes your cat SUPER dehydrated because it pulls off fluid from everywhere else and puts it into the belly) so in humans we try not to drain it often. An AST/ALT blood test (liver function tests) those would rule out that cause, however I'm not sure what a vet would do about it. In humans its managed with dietary changes (low-fat, low-protein, high-complex carbohydrate starch-based diet) and medication, but they still have the underlying problem of liver failure. Humans with ascites & liver failure do okay until their liver gets really bad - which could be years.
A tumor is also a possibility - but especially with the fluid - you won't be able to feel anything. I don't know how vets usually work that up. Your vet was likely thinking of a soft-tissue tumor, and an x-ray probably wouldn't show that unless that cat also had intestinal obstuction or something. Plus, with the fluid, it would be harder to see on xray. So it's good you avoided that. Heart failure is another story. If you have left heart failure - you mainly get fluid in the lungs & your cat would be short of breath & you could hear that the breathing doesn't sound clear if you put your ear next to their rib cage; right heart failure you could get ascites - but only because the blood backs up to the liver (kinda the same mechanism as liver failure).
If its infectious, the abdomen would be tender and the cat would likely have a fever (doesn't sound like she has this)
With regards to the weight - your kitty may have lost weight (actual mass) but regained it in fluid weight - making you think she didn't lose weight.
In any case, I agree with all of the above. "Cuddling a lot on the couch" therapy. Speaking of which, I'm going to go cuddle with my own sick kitty.
I hope yours pulls through.