Thank you very much, Linda!
This check almost does what I want. I just need to fine-tune the exact weight I want to test for. 
Currently the code I have in zones.php is:
Code:
/**
* @package shippingMethod
* @copyright Copyright 2003-2006 Zen Cart Development Team
* @copyright Portions Copyright 2003 osCommerce
* @license http://www.zen-cart.com/license/2_0.txt GNU Public License V2.0
* @version $Id: zones.php 6347 2007-05-20 19:46:59Z ajeh $
*/
...snip...
class zones {
var $code, $title, $description, $enabled, $num_zones;
// class constructor
function zones() {
$this->code = 'zones';
$this->title = MODULE_SHIPPING_ZONES_TEXT_TITLE;
$this->description = MODULE_SHIPPING_ZONES_TEXT_DESCRIPTION;
$this->sort_order = MODULE_SHIPPING_ZONES_SORT_ORDER;
$this->icon = '';
$this->tax_class = MODULE_SHIPPING_ZONES_TAX_CLASS;
$this->tax_basis = MODULE_SHIPPING_ZONES_TAX_BASIS;
// disable only when entire cart is free shipping
if (zen_get_shipping_enabled($this->code)) {
$this->enabled = ((MODULE_SHIPPING_ZONES_STATUS == 'True') ? true : false);
}
// disable for one master_categories_id
if ((IS_ADMIN_FLAG == false && $_SESSION['cart']->in_cart_check('products_id','8') > 4)) {
$this->enabled = false;
}
if ((IS_ADMIN_FLAG == false && $_SESSION['cart']->in_cart_check('products_id','9') > 0)) {
$this->enabled = false;
}
if ((IS_ADMIN_FLAG == false && $_SESSION['cart']->in_cart_check('products_id','112') > 0)) {
$this->enabled = false;
}
if ((IS_ADMIN_FLAG == false && $_SESSION['cart']->in_cart_check('products_id','111') > 2)) {
$this->enabled = false;
}
if ((IS_ADMIN_FLAG == false && $_SESSION['cart']->in_cart_check('products_id','119') > 2)) {
$this->enabled = false;
}
if ((IS_ADMIN_FLAG == false && $_SESSION['cart']->in_cart_check('products_id','120') > 0)) {
$this->enabled = false;
}
// CUSTOMIZE THIS SETTING FOR THE NUMBER OF ZONES NEEDED
$this->num_zones = 5;
}
// class methods
function quote($method = '') {
global $order, $shipping_weight, $shipping_num_boxes, $total_count;
$dest_country = $order->delivery['country']['iso_code_2'];
$dest_zone = 0;
$error = false;
... snip ...
I'll now take those checks out and just test for weight.
Thanks again,
Humberto