How to set the default value of remember me in the persistent login module to on? The persistent login module 
gives a "Remember me" at login. 

How to set this value default on?
It does not look like that module offers such a setting by default, so you'll have to change the option using hook_form_alter as well (in a custom module).

/**
 * Implements hook_form_alter().
 */
function mymodule_form_alter(&amp;$form, $form_state, $form_id) {
  // I don't check for the specific form here, since we do have a specific element we can look for.
  if (isset($form['persistent_login'])) {
    $form['persistent_login']['#default_value'] = TRUE;
  }
  if (isset($form['account']['persistent_login'])) {
    $form['account']['persistent_login']['#default_value'] = TRUE;
  }
}


You will have to make sure that your custom module is run after the persistent login module:


How to update a module's weight
There's a module for that