1-retrieve-post-comments.php

<?php $comments = $this->load_post_comments(); ?>

<?php foreach ( $comments as $comment ) { ?>

  <label for="acme-comment-status-<?php echo $comment->comment_ID ?>">
	  <input type="checkbox" name="acme-comment-status[<?php echo $comment->comment_ID ?>]" id="acme-comment-status-<?php echo $comment->comment_ID ?>" />
	  This comment has received a reply.
  </label>
  
  <p>
	  <em><?php echo $comment->comment_author; ?></em>:
	  <?php echo $comment->comment_content; ?>
  </p>

<?php } ?>

2-save-post-comment-status.php

<?php
	
add_action( 'save_post', 'acme_comment_status_save_post' );
/**
 * @param    int    $post_id    The ID of the post that's currently being edited.
 */
function acme_comment_status_save_post( $post_id ) {
	
	/* Code to verify that the user has permission to save the post has been removed
	 * for brevity.
	 */
	
	// If there are any values saved in the 'Published' input, save them
	if ( ! empty( $_POST['acme-comment-status'] ) ) {
		
		/* Additional sanitization should occur here before actually saving the array. */
		update_post_meta( $post_id, 'acme-comment-status', $_POST['acme-comment-status'] );

	}
	
	/* Code for deleting the post value has been removed for brevity. */
	
}

3-retrieve-post-comments.php

<?php $comments = $this->load_post_comments(); ?>

<?php foreach ( $comments as $comment ) { ?>

  <?php 
  
    // Retrieve the comments and determine if the ID of the current comment exists in the array
    $comments = get_post_meta( get_the_ID(), 'authors-commentary-comments', true ); 
    $is_checked = array_key_exists( $comment->comment_ID, $comments ) ? 'checked="checked"' : '';
    
  ?>

  <label for="acme-comment-status-<?php echo $comment->comment_ID ?>">
	  <input type="checkbox" name="acme-comment-status[<?php echo $comment->comment_ID ?>]" id="acme-comment-status-<?php echo $comment->comment_ID ?>" <?php echo $is_checked; ?> />
	  This comment has received a reply.
  </label>
  
  <p>
	  <em><?php echo $comment->comment_author; ?></em>:
	  <?php echo $comment->comment_content; ?>
  </p>

<?php } ?>