@JetAviator7, The simple shopping cart doesn’t have weight based shipping option. You can use PayPal’s profile based shipping which allows you to achieve this.
If you want to use PayPal’s profile based shipping then you just have to do a small tweak in the cart. Find the following line in the “wp_shopping_cart.php” file and remove it:
$form .= "<input type="hidden" name="shipping_1" value='".$postage_cost."' />";