If you are using multiple carriers for your shipping methods, you can control the order they display on your customer checkout screens.
Shipping Method Display
This can be specified in your store's Shipping Settings page.
Go to Settings > Shipping and look under "Shipping Settings" to click on the Edit Settings button.
On the page that loads, look for the "Real-Time Shipping Settings" section and click on the Hide/Show icon to the far right. This action will display the store's list of integrated shipping carriers including UPS, FedEx, USPS and others.
To the far left of each listed carrier, you will see a four-way arrow/drag and drop icon that can be used to drag the carriers to a specific display order.
2. Click on the drag and drop icon and arrange the carriers into your preferred sorting order.
3. Click Save at the top right of the page once you're done.
If you are using and sorting Custom shipping methods (by weight, by quantity, etc.), you will see a "Show Settings" link listed to the far right of the Custom option. If you click this link, you'll be able to add a special header to the Custom Shipping Methods so that they display separately from the carrier methods.
When shopping your store, customers will see the shipping method display following the sorting order you specified.