I've just rendered a video in the VSE, and the output is 14.8 MB. When I use the option to "Prefetch frames" with Proxy Render Size set to Scene render size, or even "No proxy, full render" the memory consumption goes up to 6.33 GB. That's fine for me, I have the memory to spare for these short videos, but I am curious to know if this is an artifact of the method chosen by Blender developers which results in a huge waste of RAM, or if all video editors suffer the same problem of showing previews 4000 times larger than their rendered result.
The VSE is not an efficient tool at all. It's archaic design will use a lot of resources and will limit the responsiveness.
Note that the final output size has nothing to do with the resources needed to get there, the output is compressed, but blender uses the full uncompressed image before compression.
For video editing you should use a more optimized tool. In this day and age dedicated video apps are way more efficient and responsive than blender.
But if you still want to put yourself through the pain of using the VSE check out this post: