How do we charge a customer per item/service each time it exceeds a certain weight?

Weight Per Item/Service rules can be created to accomplish this goal.

An itemized pickup needs to be performed so every item/service will then have a weight. In billing, create rules based on Weight Per Item/Service. Then put in your desired "from" weight and a "to" weight of "All". Any item/service that fits into this weight tier will then be billed whatever you desire for that item/service. Create these rules across any items/services and rule classes you need.