Thanks for sharing that screenshot. I can see that there are some gaps in your weight-based shipping rates, so perhaps this is why the customer isn’t seeing any of your rates on checkout. You can review the table below for an example of a working weight-based shipping rate:
So in your case, you’d want to look into editing your shipping rates to include certain decimals:
The above is just an example of the first two rates on your store, but the rest should also be updated to follow the same format.
Have you also contacted our live support team about this? If you haven’t already done so, you can reach out to them following the instructions on my earlier reply. They’d be able to take a closer look at your shipping settings from their end and help you further with your shipping rates.