This.The most common causes for a cat to lose weight and drink / pee more than used to are kidney disease , diabetes and hyperthyroidism. These are all treatable, and in fact diabetic cats often go into a sort of remission if the cat is put on a very low carb diet and a long-acting insulin for a while to keep their blood glucose under control so their pancreas can start to heal. then they can just be kept on the low carb diet and stop the insulin.
Yeah I agree, it is a good idea to take him for a vet exam with a senior cat lab panel just to check and find if something is going on, because if he does have some health problem it is best to catch it before it gets worse.
I learned a lot from Dr. Pierson's site catinfo.org that has already been linked.
Re the cat carrier fear, I just leave a cat carrier out all the time with a blanket in it, so they see it more as a comfy little den and don't only associate it with the vet. ( actually the crazy cats i have now love going to the vet! More people to give them attention! But this also helped when i had a shyer rescue cat who did NOT like going to the vet.)
And IrinaSaK's advice about timed meals is spot on too. Especially if you have to use insulin for a while.