Now, for all those who care to follow, this is not a serious grammar question. Just a game. You may well want to reconsider and pay no heed to the rest.
1. I take this
but to (roughly) mean
otherwise than or
except (refer to sense #2
here), and I refuse to consider other meanings for the time being.
2. I assume that "You don't trust me but at all. " is a valid utterance meaning "You don't trust me except [you don't trust me] at all.", meaning "You don't trust me with the exception that there's no exception.", meaning "You REALLY don't trust me AT ALL."
I'm not going to argue for the validity of the above sentence and the interpretation I gave for it; I'm just going to assume that it's valid and that's what it means, although I'm pretty sure it's unidiomatic, to say the least.
3. Now, making it into a question, it becomes "Don't you trust me but at all?", which sounds like a rhetorical question with the intended meaning of "You should trust me a little bit at least." (NOT "You should trust me completely.", mind you).
4. We arrive now to the question that why but at all makes sense in paragraph #2 but it doesn't in paragraph #3.
I reckon, and I'm becoming convinced, that it has something to do with
at all being a negative
polarity item.
In 2, it finds its negative setting by way of symmetric reflection of what rests on the left hand side of but in what lies on its right hand side. The negation of the statement before but permeates into what comes after it and gives at all the negative setting it needs: "You don't trust me except for the fact that [you don't trust me] at all."
However, in the question form of the sentence, "Don't you trust me but at all?", there's no legitimate material on the left hand side of but to provide the negative setting that is direly needed on its right hand side: "Don't you trust me except for the fact that [? ? ?] at all?".
5. Why? Because that question should be equivalent to something like "Don't you trust me the least bit?" (refer to 3 above). Now try to find something to substitute for the ? ? ? that would give you that kind of meaning. Your mind goes back and forth to do that, but try as it might, it will never find a good substitute.
There. That's the hidden engaging, intriguing, and mind-boggling side of this almost-meaningless sentence.
I would appreciate not being pinged about this anymore, unless you've read the whole thing I posted here this time and you have a comment on how I played the game. You're free to discuss it how you like with each other among yourselves, though. :)