If you have different rates depending on the item you will need to set up each one in the ‘Flat Rate‘ shipping method and ensure it is selected on the Product itself.
First, you will need to have a Shipping Class setup:
Go to the menu on the left hand, under Products you will find Shipping Classes.
Give your Shipping Class a name and a description and then hit “Add New Shipping Class”
Once that is done you can go back to the Shipping Setup, Under WooCommerce Settings.
Click on Flat Rate and at the bottom of the screen click on “Add New Rate”
Choose your Shipping Class.
Give it a cost and a handling fee.
Why will you need separate shipping classes?
Imagine you sell small items but just so happen to have one large item you want to sell on your site. You obviously cannot charge the same as you can with the small items.