setting user edit permissions
As far as I can see, there isn't a module that allows to the users listed in a user reference field to edit the user account where the field is contained.
You should write your own module.

The easier step is to alter the access callback for the user edit form, and use a function that checks the value of that field, comparing it with the value of the user currently logged in.

function mymodule_menu_alter(&amp;$items) {
  if (isset($items['user/%user/edit'])) {
      $items['user/%user/edit']['access callback'] = 'mymodule_user_edit_access';
  }
}

function mymodule_user_edit_access($account) {
  // The argument is the user object for the user profile being edited.
}


The default access callback is user_edit_access() which should be always called to verify that the currently logged in user has still the permission to edit the user profile, even if the user is not listed in the user reference field; users with the permission to administer users should always be allowed to edit a user account.