How to add weight to the total weight of the order witn Commerce Shipping with rules?
You should implement this hook in a custom module:

/**
 * Allows modules to alter the weight that has been determined for an order.
 *
 * @param &amp;$weight
 *   The weight field value array representing the weight of the order or NULL
 *   if no weight has yet been determined.
 * @param $order
 *   The order object whose weight is being determined.
 * @param $unit
 *   The unit of measurement to use for the returned weight of the order.
 *
 * @see commerce_physical_order_weight()
 */
function hook_commerce_physical_order_weight_alter(&amp;$weight, $order, $unit) {
  // No example.
}