Thanks to everyone who contributed to the solution. I made a couple slight changes to accomplish this in 4.5.x using One Page Checkout.
In /shipping/shipping.php add
Code:
$smarty->assign("total_weight_shipping_valid", $total_weight_shipping_valid);
after
Code:
$total_weight_shipping_valid = func_weight_shipping_products($cart['products'], true, $all_products_free_shipping, false);
I called it on /skin/common_files/modules/One_Page_Checkout/Summary/cart_totals.tpl by just inserting a row where I wanted it to display.
Code:
<tr>
<td class="total-name">{$lng.lbl_weight}:</td>
<td class="total-value">{$total_weight_shipping_valid} lbs</td>
</tr>