No, by default the picklist in Shopware 6 does not show any weight, neither the item weight per line item nor a total weight of the order. However, you can add your own column for the weight with the document editor, without a custom plugin and without entering the weight again for every order.

For each line item, the picklist shows the columns Bin location, Product number, Product name, Quantity, and Done. It does not contain any data on weight, dimensions, or packaging.

You add a column for the weight in the document editor. To do so, open the picklist under Settings → Handel (Commerce) → Documents and click Design the document.

The easiest way is to describe the change with Pickware AI, for example: "Add a Weight column to the table with the weight of the product." You can find out how this works in Customizing document templates with Pickware AI. If you are familiar with Twig, you can also customize the table yourself in Expert mode, see How do I customize my order documents with the document editor?

The picklist takes the weight from the product data. You maintain it once per product in the product properties on the Spezifikationen (Specifications) tab, in the Produktma\u00dfe (Product dimensions) section, in the Weight field (in older Shopware versions, the section is called Ma\u00dfe & Verpackung (Dimensions & packaging)). You can find out which other product data you can maintain in Which product information can I maintain with Pickware?