You can use curl_getinfo()
function to get the remote file size.
$ch = curl_init('http://www.google.co.in/images/srpr/logo4w.png');
curl_setopt($ch, CURLOPT_RETURNTRANSFER, TRUE);
curl_setopt($ch, CURLOPT_HEADER, TRUE);
curl_setopt($ch, CURLOPT_NOBODY, TRUE);
$data = curl_exec($ch);
$size = curl_getinfo($ch, CURLINFO_CONTENT_LENGTH_DOWNLOAD);
curl_close($ch);
echo $size;