There is a minimum weight and the Shopify products must weigh more than 1g.
Shopify has a rule where products less than 0.4 grams will be calculated as 0 grams and any products from 0.5 grams to 0.9 grams will be counted as 1 gram.
This means that anything between 0.5 to 0.9 grams is equivalent to 1 gram.
So, please do not enter anything less than 0.4 grams if you would like the shipping rates to show up for the product.