The new charge rule should be working with the internal weight of the cart. This weight is calculated when the cart is displayed, and if the weight triggers your charge rule then you will see the charge for it.
The charge rule should dot display a charge for the shipping if the condition for the rule is not met. As a test of this you can create a new test page and add only a cart display to the page. When you add in the cart display step through each of the steps and for the charges, discounts, shipping and tax select to show individually. To test the page add an item to the cart then visit your new test page. It should let you know what charge rules are active by name so that you can tell for certain what rule is being triggered.