OP; I think, deep down, that you know the answer to your question. When you're having to carry him up and down the stairs, it's time to say goodbye. Your dog's quality of life has deteriorated now and, in my opinion, it isn't fair to prolong it. Yes; I get it. You love your dog, and would do anything for him. But, without wanting to sound like a twat, that is irrelevant. The dog's welfare is paramount now. Do the right thing by him.
It's heartbreaking when these decisions have to be made. I've been through it a few times, and it's like a dagger through the heart