Need help narrowing disease ideas. Vet wont do.

My kitten is 5 weeks and 3 days old. He's huge for his size. He's about the size of a 9 week old kitten. I'm thinking it's a pituitary gland tumor like in humans which can cause rapid growth. He's also deaf.
Extra info. His mother is a small cat and he was a liter of one. His eyes opened at 1 1/2 week old. He went from Tiny peanut to the size of a 3 week old kitten in a week. He seemed to rub his ears a lot when small I thought it was just them being itchy but with the deafness I'm not sure. He's been to the vet whom I had to argue his age with. I helped birth him was there I marked in on a calender along with his markings and took a photo. I KNOW his exact age. They won't do any tests unless I allow them to do a full spectrum which is like 10k or more. I opted for choosing which exact tests to do. Which they agreed but I need to have an idea of which ones because lab fees check up fee them the actual tech and test fees are all separate unless I do all the tests at once(trying to lesson the blow to my wallet) so any ideas what can cause deafness and rapid growth in a 5week old kitten. He also has blue eyes but that could also be his eyes havnt changed yet. Picture attached.

this was him at 3 weeks my hands about 8 1/2 inches from palm to tip.can't tell in picture but he's much bigger than my hand by about 2 to 3 inches

Maybe his father was a very large cat and there's nothing wrong with him. There was a litter of five at the shelter last year with three enormous kittens, easily twice the "average size" although mom was a dainty cat. Mom was fostered, so we had the exact date of birth, but the 3 males seemed to be weeks older than they actually were, not only in size but in development. I saw two of them just last week, and they're both around 20 lbs with huge paws.

If he's got no health problems other than deafness and is developing properly, it'd probably be best to just wait and see.

I adopted my now two year old cat when he was 7 weeks old.  At around 3 months old he grew into an adult cat.  He started growing so fast I we were beginning to wonder if we had adopted a baby panther instead of a black domestic short-haired kitten.  After that his growth slowed down and he the size of a normal two year old cat now.  Your baby may have just hit a growth spurt.