Is a person's inquiry into the possibility of the name of majesty, "Allah," being one of the "names of 'illah (cause/reason)" considered disbelief, disparagement, or contempt, knowing that the inquiry arose after hearing a grammatical example: "Allah increases the doers of good"?

Our advice is to disregard obsessive thoughts, because your question is not intended to diminish the name of Allah. The weak letters (vowels) are waw, alif, and ya. They are called weak letters due to their frequent change and alteration from one state to another, by way of omission, addition, deletion, substitution, and inversion. Weak letters change by one of them being transformed into another due to various linguistic phenomena.