Premiere doesn't just splice up existing media clips and put them together. It re-encodes a video from scratch. That means it doesn't care what footage you are putting in, you are building a whole new video from the ground up. You could be starting with a super low quality video like a zoom recording, or you could take footage straight from the camera of a Hollywood Blockbuster. It's just data. When you export, you are telling Premiere what the export settings are, including what the bitrate is.
File Size = Bitrate * Time
If you figure out what the bitrate of your source media is, you can try to match that, but that's also not advisable since you are adding another layer of compression to a likely already aggressively compressed video. Maybe you can think of it like this: You have a video clip that has already had 50% of the data (quality) removed from it. If you apply the same bitrate to that, you are also running it through the same compression algorith, so you are removing 50% of the quality from that video again. When you have already compressed media to begin with, you need to actually increase the bitrate just to hold on to what quality is left. If you don't care about the quality and the file size is more important, you can figure out the bitrate and match that. (You can use a program like Media Info to see the bitrate, or just do the math.)
If you really want to just make basic cuts and have them sort of "glued" back together without any re-encoding, you probably want to look into a muxing application of some kind.
Also, your match sequence settings checkbox is not doing what you are hoping it's doing. You are getting the resolution and framerate from the sequence, but to be honest I'm not entirely sure what it's pulling for any bitrate. You likely don't want to be exporting to that format either, your intention is probably the H264 format. That top checkbox is more typically used alongside preview files that you've set up in your sequence settings.
Thank you so much for your quick and clear reply. This makes total sense. Yes, in the case of these videos, they are screen captures and as long as the audio is clear and the image not pixelated I am happy. I will try another software that can just 'split and spit' for quick edits and leave Premier for the quality-oriented works. Thanks again! Still, I am going to look into Media Info just to learn some more about the bit rate and figure it out. Cheers 🙂
No worries. The Tree View in Media Info is where you'll find a lot of info. It's a handy app to have if you're working with media. I wish I had some recommendations on specific software that would do the remuxing, but I haven't really done much work with that intention. But you can see in the case of video editing software like Premiere, you want to start with as high quality of material as possible. Plenty of people still use it to edit zoom videos and that kind of thing, you just either have to accept that the quality is going to deteriorate at the same or lower bitrate, or the file size is going to be larger than you started with.