Coughing cat.

My cat has had a horrible cough for two or three months and the vet doesn't know why. He coughs for 3-10 minutes at a time several times every day. His breathing is visibly labored, his sides look like they're forcefully contracting. When it's quiet and he is laying on me I can hear his breath sounds weezey. At first I thought it was a hairball but nothing ever came out. The first vet gave me hairball medicine, which didn't help at all. I also put him on a hairball and weight control diet because he was overweight which I thought might contribute to some respiratory problems. It has gotten worse. I took him in for an x ray, it showed his kidneys were slightly enlarged. This time the vet said he is too skinny, so I have been feeding him two cans of food per day in addition to his regular hard food. He gets excited to eat the canned food, but he never finishes it. He is urinating, but there isn't feces in the litter box now. I am extremely concerned because a little over a month ago I had to put my other 3 year old cat to sleep because his liver and kidneys were failing and the vet didn't know why. His symptoms were different though, he had very runny eyes, while Asiago's eyes are fine right now. But my other cat also became very skinny and his muscles atrophied until he couldn't stand up. I'm hoping Asiago's weight loss is just because of the diet, or maybe he is a little depressed about his brother dying recently. Asiago has been extra sweet since, and wants to play. He doesn't go outside, except on a balcony. I'm sure he eats bugs out there, and I have a bird feeder he loves to watch, but cannot get to. I also have two rabbits with whom he shares a water bowl. I have no idea what is relevant, so I'm just throwing everything out there. As far as Asiago's medical records go, he was exposed to herpes by my other cat, however, he has not had any symptoms of it since he was less than a year old. The vet's tests for for leukemia and heart worms, and some other worms I can't remember were negative. His blood cell counts were normal, and I have the blood work from the most recent vet visit. The following are the results that turned up abnormal. The vet pointed out most of these are just barely outside normal range and therefor probably not alarming of helpful.

LaserCyte:
HCT 50.4% normal: 30 - 45
HGB 15.1 g/dL normal: 9 - 15.1
EOS 1.00 normal: 0.10 - 0.79
PLT >163 K/uL normal: 175 - 600

Catalyst Dx:
CA 12.3 mg/dL normal: 7.8 - 11.3
ALB 4.0 g/dL normal: 2.2 - 4.0
ALKP <10 U/L normal: 14 - 111
TBIL 1.0 mg/dL normal: 0.0 - 0.9