The delivery cost can be set based on the weight of the products. The cost can increase gradually with the weight increase of the order. In order to use this function the weight needs to be set for every single product in the shop, unless this has already been done. Note: If no weight is set, the weight will be seen as zero for that product.
Create a new delivery method
Create a new delivery method on the Settings > Delivery and payment > Delivery method page. Write the name you would like to use for the new method in the empty field on the last row and choose "Weight of the products in the shopping basket" as the "Type" in the drop down menu and save.
Specify the delivery method settings
Open the new delivery method by clicking it's name and go to the Settings page. Specify the weight limits and corresponding prices.
Choose which weight unit you would like to use, for example pounds, from the drop down menu. Save the first row of the weight limit and the price. Once saved a new row will appear in order to fill in the next weight limit and so on.