Syntax for referenced variables in hook_commerce_physical_order_weight_alter?
If your hook_commerce_physical_order_weight_alter is not fired (remove if to double check that it's not), check if commerce_physical_order_weight() is fired as alter hook is right at the end (so add dpm() or die() at start of the function):

    function commerce_physical_order_weight($order, $unit = 'lb') {
      // ...
      // Allow other modules to alter the weight if necessary.
      drupal_alter('commerce_physical_order_weight', $weight, $order, $unit);



if it is not fired, that means the problem is somewhere else, so check if commerce_physical module is enabled and configured properly and you've the right dependency to it,
if it is fired, then check that:


your module is exactly called add_shipping_weight,
the module file included (add hook_init() or die() to check)
clear your caches (Drupal caches, memcached/redis if used, etc.), so list of hooks can be updated (it's a common mistake)