In Drupal 8, module's weight is stored into ConfigFactory. Here's how to get or set module weight.

Get module weight:

<?php
  $extension_config
= \Drupal::configFactory()->getEditable('core.extension');
 
$module_weight = $extension_config->get("module.MODULE_NAME");
  echo
$module_weight;
?>

Set module weight:

<?php
  module_set_weight
('MODULE_NAME', 100);
?>
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