Why are you using AE to do an editing job? That's now what it's for.
Dave is right. You should be using Premiere.
That being said, your basic understanding of how AE works on a fundamental basis is flawed.
You rendered an uncompressed video from After Effects. It will be larger than the VERY compressed video from YouTube. AE works with completely uncompressed video information for every pixel on every frame. The file size of the incoming video is irrelevant. AE will always work with completely full frame, uncompressed information. If you feed it a highly compressed video source, it decompresses it while you're working.
Think about it this way, you can have nothing in your project but a 23 kb JPEG and make a video with it and the result will be a huge file if you render an uncompressed video.
The file is big because you don't understand how compression works and you haven't taken the time to learn how to use After Effects. From this forums FAQ:
As Dave said, you're using the wrong app. AE is specifically designed to create shots or short sequences that contain visual effects or motion graphics.
is specifically designed to create shots or short sequences that contain visual effects or motion graphics. If you want to edit then you should be using Premiere Pro.