What does it mean when people ask 'Do you have a credit card, at all'?
I do not know whether this is correct and have nothing with which to back it up, but it is too long to go in a comment, so it’ll have to be an answer.
Personally, I would suspect that this is perhaps a usage that has spilt over from Hiberno-English.
In my experience, a more or less semantically void ‘at all’ is often used in Ireland as a fairly generic closing statement in questions (much like ‘right’ or ‘innit’ are used to make statements into questions). “Do you see him at all?” just means, “Do you see him?”. If ‘at all’ should be taken literally, it is sometimes doubled: “Do you see him at all, at all?”.
As far as I am aware (though again I’ve nothing to back it up with), the Irish usage comes originally from the way the phrase ar bith (meaning both ‘any’ and ‘at all’) is used in Irish, which differs somewhat from English ‘at all’. Overuse of an expression common in one’s native language when speaking a non-native language is very common, and this is originally one such case.
An bhfuil airgead ar bith agat? = Do you have any money?
Ar chodail tú (ar chor) ar bith? = Did you sleep at all?
An bhfaca tú ar bith é? ≈ Did you see him any?
An bhfaca tú ar chor ar bith é? = Did you see him at all?
From these examples, where ar bith sometimes means ‘at all’ and sometimes ‘any’, it is fairly easy for an Irish speaker learning English as a second language to overuse ‘at all’, leading to cases where ‘at all’ really just means ‘any’, or even less than that (“Did you see him any?” is not a very natural phrase, and English would just have, “Did you see him?”).
Ar chor ar bith (which unambiguously means ‘at all’, never just ‘any’) in Irish is a kind of ‘doubled expression’ in sound (ar X ar Y), so once ar bith was fairly solidly identified with ‘at all’ in English, I suspect it was rather a simple matter of simply creating a doubled expression in English to match the Irish one, and ‘at all at all’ was born.
The doubled expression has not (yet?) made it into British English as far as I know, but I don’t think it far-fetched to hypothesise that the weakened and seemingly improper use of ‘at all’ is something that comes from Hiberno-English.
In the U.S., appending an "at all" at the end of a question can have one or more of four shades of signification:
a betrayal of a mild irritation ("Do you have any form of payment at all?");
after a verbal exchange of some length, an attempt to conclude the exchange by extracting a definitive reply of some type ("Do you have anything to write this number on at all?");
a request of one to another to provide even the smallest of contributions to the matter at hand ("Class. Don't any of you have anything to say about this poem at all?"); and
a conveyance of doubt of one person that the other ever satisfied a particular requirement, when the second person is attempting to conceal that fact that he did not ("Is it true that you never had any intention of completing this at all?).