I set something similar to this up using Table Rates.
I set it to the minimal weight (has to be greater than .2, if I remember correctly), then I made changes to
to suit the needs of this client:
If you have to use an online CC processor, you could configure the email invoice (order status) to include a link for them to make thier payment.
define('MODULE_SHIPPING_TABLE_TEXT_DESCRIPTION', 'Table Rate');
define('MODULE_SHIPPING_TABLE_TEXT_WAY', '<b>Your order is over 500lbs.</b><br><br>Please select this shipping option and our customer service department will select the best possible shipping method for you. When checking out, please choose either <b>Offline Credit Card Processing</b> or <b>Check/Money Order</b> and we will send you an updated invoice showing the actual shipping cost. If you select to pay with a credit card, your order will not be charged until we receive approval of the shipping charges from you. If you choose to send a check or money order, your approval will be assumed upon receipt of payment.<br><br>If your shipment requires any special instruction, please include those in the comment box on the Checkout Step 2 page.');