Спасибо! Вопрос решен!
Нашел прекрасную функцию в интернете:
function remote_filesize($url, $user = "", $pw = ""){
ob_start();
$ch = curl_init($url);
curl_setopt($ch, CURLOPT_HEADER, 1);
curl_setopt($ch, CURLOPT_NOBODY, 1);
if(!empty($user) && !empty($pw))
{
$headers = array('Authorization: Basic ' . base64_encode("$user:$pw"));
curl_setopt($ch, CURLOPT_HTTPHEADER, $headers);
}
$ok = curl_exec($ch);
curl_close($ch);
$head = ob_get_contents();
ob_end_clean();
$regex = '/Content-Length:\s([0-9].+?)\s/';
$count = preg_match($regex, $head, $matches);
return isset($matches[1]) ? $matches[1] : "unknown";
}