Hyde here from Shopify.
I'd need to get a better sense of your store set up to help. Could you provide me with a link to your store so I can test out the checkout myself? Could you also, please, tell me more about what shipping rates you have set up?
Are your shipping rates based on the weight or price of the order? If it is weight-based, have you input the weight for each product so that the shipping can be presented accordingly at checkout? There's more on this here, but I look forward to hearing more from you so that I can help you out.
All the best, Hyde.