How to display sorted posts in the ‘All Posts’ page

I think this is what you want…

This isn’t tested so you may have to fiddle with it.

in your functions.php file, add something like this :

EDIT (2)

After rereading, I saw you’re not using custom post types, so i’ll change my code accordingly. I don’t know how to detect when you’re on the ‘manage all posts’ page, so maybe someone can complete my 'if' statement.

This should work.

 function set_post_order_in_admin( $wp_query ) {
      if ( is_admin() ) {
           if( 'edit.php' === $GLOBALS['pagenow'] ) { 
                $wp_query->set( 'orderby', 'menu_order' );
                $wp_query->set( 'order', 'ASC' );
           }
      }
 }
 add_filter( 'pre_get_posts', 'set_post_order_in_admin' );