Reduce render file size in After Effects
You need to change the encoding settings. By default, AE uses the AVI animation codec, which is very good at retaining quality but creates incredibly large files. Using an intermediary codec like Apple Prores, Avid DNxHR, or GrassValley HQx would give you visually equivalent quality with a significantly smaller file size.

If that file size isn't small enough for you, then you may want to go to a compressed codec like h.264. Choosing h.264 with a bitrate of around 20-30Mbps would give you pretty good quality. The disadvantage of going to h.264 is that you'll lose a lot of visual information, making any additional editing such as color grading more difficult. You'll also be using a multi-frame encoding which makes scrubbing through an editing timeline very difficult.