You can vary your shipping costs by product type by creating shipping variations. For example, you can create one shipping variation for large items and one for small items, assign products to them and then define different costs to those variations. Your shop starts with one shipping variation called DEFAULT which all products are assigned to unless otherwise specified. You define your base pricing in the DEFAULT shipping variation and then  override those costs for your other shipping variations.
Creating a Shipping Variation

1. Go your shop's Manage area
2. Click on the Settings Tab and select Ecommerce 
3. Then choose Shipping on the lefthand side
4. Click on Add/Edit Shipping Variations. 
5. Type in the name of your new variation.
   
6. Click FINISH.
7. You will see the new shipping variation listed.
   
8. Click on the new variation and edit one of the shipping methods. You will see that you can override the default pricing, increasing or decreasing the price as desired.