By default, Drupal uses an absolute path, and will insert your domain name into the path to your JS and CSS files.
You can override this, in template.php, like so:
function YOURTHEME_process_html(&$vars) {
//convert absolute URLs (https://www...) into relative (/some/path) for JS and CSS only
foreach (array('scripts','styles') as $replace) {
if (!isset($vars[$replace])) {
continue;
}
$vars[$replace] = str_replace("https://stage.example.com", '', $vars[$replace]);
$vars[$replace] = str_replace("https://www.example.com", '', $vars[$replace]);
}
}