To display Webshipper rates, third-party rates need to be enabled
What is it?
To display your shipping rates directly in your checkout, you need to enable a feature in Shopify called "Third-party calculated shipping rates". This is a subscription limitation set by Shopify.
While the option is included by default in an "Advanced Shopify" subscription, you can contact Shopify support and instantly have it enabled for a smaller plan.
You can do so for an added cost of $20 per month or for free if you are paying for your subscription on an annual basis.
Do I already have it?
Check if you have it enabled here: https://your-store-name.myshopify.com/admin/settings/shipping
If you see the shipping truck, it is not enabled and you will need to contact Shopify.
Inform them of the following: "I wish to enable third-party-calculated-shipping rates".
You will need to re-install the Webshipper plugin, if it was installed
before you activated the third-party rates on your Shopify account.