I realize I'm a little late to the game on your post, but if you're still in the market for a solution we have an app called Automate Shipping Profiles that does exactly this. Using our Profile Conditions system, you can choose how products are to be assigned to your shipping profiles and even adjust the priority for which profile conditions rank higher.
The app is free to install and set up. Once you're ready to enable automation, you select a plan based on the number of products you have in your shop. Once you've authorized the billing plan, you can run a Bulk Update of your product catalog to automatically assign products to their corresponding shipping profile. Once the bulk update is complete, our system sits in standby and listens for any changes to your product catalog or collections. If a change is detected, it will perform a new conditions check on the updates product/collection ensuring your shipping profiles are always up-to-date.
Let me know if you have any questions.