Ok, I got it to echo the value on the cart page and I assume that you could remove the echo part, with the following code:
<?php echo ($MyCartName->TotalColumn("TotalWeight")); ?>
THEN on the confirm page changed the code for the shipper to:
$Shipping_PackageArray[$Shipping_PackageIndex]["PackageWeight"] = "".$MyCartName->TotalColumn("TotalWeight") ."";
This will total all of the item weights if shipping in one box. I used an average size of shipping box as most costs are mainly factored by weight.