However, unless it is actually INVOICED, values and weights are not totalled.
That's not quite true. The issue is that Extended Price and Extended Weight are calculated based on the value of Quantity Shipped, not Quantity Ordered. But you don't have to invoice an order so that you can save an order with Qty Shipped <> 0.
In the OE Company Profile, enable the option 'Qty shipped on orders'. This allows you to choose posting either as an order or an invoice while having a qty shipped <> 0. In addition, to prevent accidental posting of an invoice, there is another option 'Default posting to order' which in the above scenario will select 'Order' as the default document type to post.
After posting an order with qty shipped <> 0, you can print a pick slip or order confirmation specification with the Extended Weight and Price for each item, and a grand total for weight/price for the entire order.
Would this solve your situation?