Karlie here from the Shopify Guru Team! The order weight is calculated by adding up each of the individual weights of the products that were purchased in the order. There currently isn't a way to export the order weight, but I can let you know how you would figure out the weight of an order.
Each product should have an assigned weight. You would have added the weight to each of your products when you were creating each product from your Shopify Admin. The 'weight' section of the product page can be found in your Shopify Admin> Product page under the 'Shipping' section. To find the weight of an order, you would simply add up the weight of each product that was purchased in the order. For example, if a customer ordered 5 winter coats and each coat weighed 2 lbs then the order would come up to 10 lbs.
You can read more about how to use weight based shipping in your storefront in our handy guide and if you're needing some help figuring out what weight each product should be, be sure to follow our guide, here.
I hope this has answered your question. If not, or if you have any further questions please let me know. I will be happy to help!