Hello,
Have you activated the child theme on site (Appearance > Themes)?
Try to check if this function does not work at all from child theme, you may just echo ‘some text’; in the function to see if it works. If so then it could be wc_add_notice function causes the problem and try to add next strings
add_action('wp_ajax_add_transfer', 'check_cart_weight');
add_action('wp_ajax_nopriv_add_transfer', 'check_cart_weight');
If the problem woun’t be solved, provide temporary wp-admin access and describe in more details how to recreate (what dares to do to see how it works).
Regards