Well If it was an A330 no probs landing over weight as long as you keep it less than 360 fpm on touchdown.
Engineers can sign it off easily. ( in fact if it's below 360 fpm I don't think any special checks are required? )
Printout of the landing data is available after shutdown.
My mob would be mighty annoyed if I wasted an hours gas reducing LW.
Must be more to the story?