Is there a way I can export videos with relatively the same byte-size as their original? Whenever I edit, I notice that the mp4 files have a smaller combined file size than the video I export. Is there a setting or function I'm missing when I want to publish a video?
If you're using H.264 for your export, Premiere isn't the slickest at setting encoding options. For some users, they export a ProRes or DNx file as a master from Premiere. Then use Handbrake, ShutterEncoder, or ffmpeg to take that and create H.264 files for more options to keep quality from notably suffering while shrinking file size.
That said ... the base thing about file-size is bitrate times file length. Go to a smaller bitrate, the file will be smaller.