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:
$extension_config = \Drupal::configFactory()->getEditable('core.extension');
$module_weight = $extension_config->get("module.MODULE_NAME");
echo $module_weight;
?>
<?php
module_set_weight('MODULE_NAME', 100);
?>
module_set_weight('MODULE_NAME', 100);
?>