Most of the shipping providers require that the weight be at least 1 pound. You con force a total weight of under a pound to be 1 pound by editing the line that passes the weight.
change:
$Shipping_PackageArray[$Shipping_PackageIndex]["PackageWeight"] = "".WA_eCart_FormatNumber($<your cart name>->TotalColumn('TotalWeight'), true, 1) ."";
to:
$Shipping_PackageArray[$Shipping_PackageIndex]["PackageWeight"] = "".WA_eCart_FormatNumber((<your cart name>->TotalColumn('TotalWeight') >= 1)?$<your cart name>>TotalColumn('TotalWeight'):1, true, 1) ."";
where <your cart name> is the name of your cart object.