I have already set up custom shipping rates for other countries, but these do not show up in checkout. I also then tried to add general shipping rates based on weight for these countries but none of them show up in the list.
Is there something I’m missing to enable international shipping?
Is this what you are meaning, or are you referring to something else?
If your store has access to Shopify Markets, you can also navigate to Settings > Markets to check if the other regions on your store has been activated. If a region you wish to sell to isn’t currently active on your store, you can click Manage > Activate market for the market that wish to activate. This should then activate the shipping rates on checkout for those regions.
Since Shopify Markets is a new feature of Shopify, if you’re not familiar with it I’ll also link our blog here that explains this feature in more detail.