Q. How do I assign the oik weight/country shipping method to a product in WooCommerce?
A. You need to set a weight for each product and define the rates in the settings page.
The plugin calculates the shipping costs based on the total cart weight.
See oik-weightcountry-shipping – basic user guide
This answer applies to both oik-weightcountry-shipping and Multi rate weight/country shipping for WooCommerce