When purchasing fresh fruit and veges and other foods from the supermarket that are weighed during check out, I have tended to use the very thin plastic bags provided (when it's necessary to use a bag at all) because if I use my own cotton bags I'll pay extra for the privilege due to the heavier weight of the cotton.
It's not a realistic option in this case to zero the scales first with the empty bag sitting on the scales. The extra cost of using my existing cotton bags would be substantial when the produce has a high price per kilogram. eg if the bag weighs 20 grams, and I'm purchasing something at $5/kg, I'll pay about an extra 10 cents for each bag used, assuming the weight of the thin plastic bags is negligible.
It's also not a realistic option to reuse the thin plastic bags; they simply aren't very durable.
Which reusable materials/fabrics could be used for replacing these bags to minimise any extra cost? Silk is pretty light, but I'm not sure how long it would last, and there might be other options that are cheaper or more sustainable.