Calculate shipping cost by weight in Drupal commerce
For Commerce shipping 2.x this is actually pretty simple.


Create a calculation rule.
Set the condition that the weight for the order is above 2 kg (this can be a bit tricky to do in Rules, but there a plenty of guides how to do it. I believe Randy even shows this in the video you linked to.
Select the "add amount to unit price" for a line item and select the shipping line item. You can even select which component to use for this and could create an weight fee price component if you wanted to.


That's it.