Get term weight in node object for ordering with EntityFieldQuery
No, this is not possible. You can only order on actual field values, the term weight would require a JOIN to a non-field table and EFQ is not capable of doing that.

You will have to create a manual SQL query to do this. Note that Drupal by default maintains the node &lt;-> term associations in the taxonomy_index table, that one is easier and more reliable to query than a field data table.