Video size difference across different formats
You first need to tell us which software you're using. I'm assuming it's the adobe media encoder? Handbrake? ffmpeg?
Nonetheless, the filesize is determined by your resolution, framerate and bitrate. Try exporting the video with VBR with 2 passes and set the bitrate to something between 3 and 6 - that should be enough for a 1920x1080 h264.