We should persist the size of the rich:column's in an rich:extendedDataTable if they have been resized by the user. Our application moved to other pages than the page including the table. So if the user returns to the page with the table, the columns should have the resized width. In the book Practical Rich Faces on page 206 it is written
saves the state of the component between requests.
tableState should works for you. it's used successfully at demosite.