I did find a way to do this but it is not a "quick fix" so to speak... in other words you would have to manually add it to each results/list page. The way I had a working model was to use jquery's draggable sortable widget and add a save function to that which would rewrite the order weight column. I need to go purchase a jquery documentation book to see if I can write some sort of function and script where it could be quickly deployed.
See this link here: drag-and-drop-reordering-of-database-fields-sortables-with-jquery/
You would need to make your table into a list and then apply the jquery ui to it to get the desired results.