Bum bag.

Sorry, not an insult ... I think they are called "fanny packs" in the U.S. (but "fanny" is a naughty word over here and means something quite different).

You could wear it at the front and under your clothes, rather than over them. Not tried it under clothes but I often wear one when walking in the hills - I guess it depends how far your top layers of clothing extend over your tummy/hips.

Cheers, Bob.