How to Reduce/Increase module's weight on the module install process?
Use hook_module_implements_alter() rather than changing the module weight.

Sample implementation from content_translation.module:

function content_translation_module_implements_alter(&amp;$implementations, $hook) {
  switch ($hook) {

    // Move our hook_entity_type_alter() implementation to the end of the list.
    case 'entity_type_alter':
      $group = $implementations['content_translation'];
      unset($implementations['content_translation']);
      $implementations['content_translation'] = $group;
      break;

    // Move our hook_entity_bundle_info_alter() implementation to the top of the
    // list, so that any other hook implementation can rely on bundles being
    // correctly marked as translatable.
    case 'entity_bundle_info_alter':
      $group = $implementations['content_translation'];
      $implementations = [
        'content_translation' =&gt; $group,
      ] + $implementations;
      break;
  }
}