While resolution may change the size of your exported file a little, as Tero mentions, the most important thing here is the bitrate. Compressed formats don’t just save pixel information flatout, so half the pixels doesn’t always mean half the filesize.
You can increase compression by lowering the bitrate, expressed in mbit/s or megabits per second, meaning less data will be used per second of video and your file will be smaller in the end – fewer bits * same amount of seconds.
Be aware that this will decrease the quality of your overall image, so more artifacting etc may occur.