To display your shipping rates directly in your checkout, you need to enable a feature in Shopify.
The feature is called "Third-party calculated shipping rates".
This is a limitation set by Shopify and not one that we can change.
While the option is included by default in an "Advanced Shopify" subscription, you can contact Shopify Support and 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.
Once you have the feature enabled for your Shopify account, you need to create a shipping zone that makes use of the Webshipper Rate Provider as the carrier.
This way, Shopify will query Webshipper and receive the list of carriers that you have configured in your Webshipper account.
Note: You may have to re-install the Webshipper plugin, if it was already active.