You will need to touch the code that builds that ...
There is no override for this so save the original and your changes ... edit the file:
/includes/modules/pages/shopping_cart/header_php.php
Change line 42 - 44 from:
case (SHOW_TOTALS_IN_CART == '1'):
$totalsDisplay = TEXT_TOTAL_ITEMS . $_SESSION['cart']->count_contents() . TEXT_TOTAL_WEIGHT . $shipping_weight . TEXT_PRODUCT_WEIGHT_UNIT . TEXT_TOTAL_AMOUNT . $currencies->format($_SESSION['cart']->show_total());
break;
To read:
case (SHOW_TOTALS_IN_CART == '1'):
$totalsDisplay = TEXT_TOTAL_ITEMS . $_SESSION['cart']->count_contents() . TEXT_TOTAL_WEIGHT . $currencies->format($shipping_weight) . TEXT_PRODUCT_WEIGHT_UNIT . TEXT_TOTAL_AMOUNT . $currencies->format($_SESSION['cart']->show_total());
break;
You will need to adjust the Shipping estimator in a similar manner if you are using that ...