if (client.connect("http://weatherstation.wunderground.com", 80)) {
You connect to a server. The server name is NOT http://anything.
The server name is weatherstation.wunderground.com.
client.print("GET /weatherstation/updateweatherstation.php?ID=XXXXX&PASSWORD=XXXXX&dateutc=now&tempf=48&action=updateraw/ HTTP/1.1/r/n");
The carriage return and line feed characters are \r and \n.