How do I add tabledrag with 'weight' to admin form
At the risk of oversimplifying, have you tried using or integrating Draggable Views? 

If the items you are sorting are nodes (I'm not clear on this) it is a great option for achieving drag-and-drop sorting as you can assign as many fields to an entity as you'd like and set different sort priorities depending on the circumstances.  That as apposed to 'weight' which is a one size fits all number.