I can’t, for the moment, send to you the shop link but I will soon.
For my shop, the checkout page and the cart are merged.
It seems that the issue comes from this case.
Right now, I found a dirty solution… I just comment a if
File: wc-template-functions.php (~line:1574)
function woocommerce_cart_totals() {
/* Dirty "Fix" : Issue with the WBU plugin and Total info */
/* The total info isn't displayed when the page is loaded */
/* cart & checkout pages are merged */
// if ( is_checkout() ) {
// return;
// }
wc_get_template( 'cart/cart-totals.php' );
}