Menu Order is module, which helps to create the node menu entry (item) in the right location in the menu structure. In the node edit view "Menu settings" section the "Weight" field is replaced with the drag & drop table containing the "Parent item" children items. The node menu entry (item) can be dragged and dropped to the right place within the table. It works the same way in the menu link edit form.
The screenshot of the overriden "Menu settings" block is attached (mwadd-screenshot.png).
The closest module which tries to help with setting up the menu item weight in the node edit form is Menu Weight Assist.