Then you will need to write your own shipping module to do this calculation based on weight ...
Something like customize the Flat Rate flat shipping module and set its rate to 0.00 then the code change:
Code:
// class methods
function quote($method = '') {
global $order;
global $shipping_weight;
$chk_weight = round($shipping_weight,0);
//$5.35 for the first lb, + $1.25
$chk_weight_charge = ($chk_weight > 1 ? 5.35 + ($chk_weight - 1) * 1.25 : 5.35);
//echo 'I see: ' . $chk_weight_charge;
$this->quotes = array('id' => $this->code,
'module' => MODULE_SHIPPING_FLAT_TEXT_TITLE,
'methods' => array(array('id' => $this->code,
'title' => MODULE_SHIPPING_FLAT_TEXT_WAY,
'cost' => MODULE_SHIPPING_FLAT_COST + $chk_weight_charge)));
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