Hmmm that's rather baffling, typically in older cats weight loss is thyroid, diabetes, or kidneys, all of which should have shown in the blood profile. I'd say that an EKG might be a good option, they should only need to lightly tranq. the cat for that. As some have said earlier in this thread, that an ultrasound doesn't seem to require anesthesia either.

My only personal experience with a pet with a tumor was a guinea pig, he kept getting skinnier and skinnier, but his actual weight never changed one bit. Seems the tumor was growing at the same rate he was losing body mass.

Let us know what the vet says/recommends.

Good luck