When shipping is required, I bought 2 of the same product, yet the total didn't compute shipping for two items, only one item shipping was added.
There is a setting for each item make sure this setting is not checked for each item "Count shipping only once if more than one is ordered at the same time"
The group settings on an item is if you want someone to be added to a different SMF membergroup once they purchase a product.
Currently there is no setting to control the shipping cost based overall total weight but would make a good feature request. We currently have shipping conditions which allows you to set the total shipping based on the order total range.