If you do not have the "Flexible Shipping WooCommerce" plugin installed yet, please download it here.

Then go to the Plugins tab in your WordPress admin panel -> go to your WordPress admin panel Plugins section and click on "Add new". -> and click on "Upload Plugin":

After the plugin is installed and activated, go to your WooCommerce tab in the admin panel -> Settings:

Make sure, you have the Weight Based Shipping option available:

Now you can add Shipping zones and rules.

Here is an example of how to create Shipping rates for the US zone.
First, add the Shipping zone:

Name the Zone name, and add the United States in the zone region.
Then add Flexible shipping as a Shipping method:

Now, click to edit this method:

Rename the Method to "Weight based shipping" and choose the desired Tax Status:

Scroll down and add Shipping Cost Calculation Rules based on the weight and our Shipping prices:

Click Save Changes, and you are done!