I don't think Mr. Woodhouse is feigning or pretending to feel something he does not. I just think he has gotten in the habit of considering himself to be ill and so he still feels and thinks that even though there is no real infirmity there. I don't see Mr. Knightley believing he is ill so much as humouring him because what good would it do to try and talk him out of it? He's a sweet, loveable old guy and no one wants to contradict or upset him.

This thread made me think of Moliere's Imaginary Invalid (in which I had a role in our university theatre production). The title character is always consulting his apothecary. He also has two daughters, the eldest of whom wants to marry a young man her father does not approve (Instead he wants her to marry a doctor so he will always have one nearby). Certainly Argan (the imaginary invalid) is nothing like the sweet-tempered and kind like Mr. Woodhouse, but his behaviour with respect to his illness has similarities.

To himself he says "Mr. Purgon (one of his physicians) told me that I was to walk twelve times to and fro in my room every morning, but I forgot to ask him whether it should be lengthways or across."

and this little scene reminded me of Mr. Woodhouse a lot:

CLEANTE: Sir, I am delighted to find you up, and to see you better.

TOINETTE: (_affecting to be angry_). How! better? It is false; master is always ill.

CLEANTE: I had heard that your master was better, and I think that he looks well in the face.

TOINETTE: What do you mean by his looking well in the face? He looks very bad, and it is only impertinent folks who say that he is better; he never was so ill in his life.

ARGAN: She is right.

TOINETTE: He walks, sleeps, eats, and drinks, like other folks, but that does not hinder him from being very ill.

ARGAN: Quite true