I have just this minute got it working.
Basically the same function I used for determining price of the cart
items could be used for determining weight. All I needed to do was
assign my DB with a field called weight and call that instead of price
from the DB so my calculate weight function looks like this. 

function calculate_weight($cart)
  // sum total weight for all items in shopping cart
  global $weight;
  $weight = 0.0;
    $conn = db_connect();
    foreach($cart as $ItemCode => $qty)
      $query = "select weight from products where ItemCode='$ItemCode'";
      $result = mysql_query($query);
      if ($result)
        $item_weight = mysql_result($result, 0, "weight");
        $weight +=$item_weight*$qty;
  return $weight;

By making $weight a global variable I then call that in my shipping
function and set it's parameters:

function calculate_shipping_cost($weight)
  //shipping costs calc. less than 10KG is 15 more than 10KG currently
        global $shipping;
        if ($weight <= "10000")
        $shipping = "15";
        $shipping = "20";
        return $shipping;


I still don't fully understand why this works but am happy it does!

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