Export as a gif

I must admit, when I've had tight deadlines for GIFs, I resort to rendering out H.264 MP4 files and using Giphy.com to convert them.  Plus when you upload them, there's an option not to share them, then I just download the result.  It's proved to be quicker for me and the files are always super small.  

As Roland already suggested, rendering GIFs directly from AE is less than ideal. Take a detour via PS or have your GIF created by one of the gazillion alternative tools or web sites based on converting/ uploading a clip you rendered from AE.

Mylenium

You get more controls/options and smaller GIFs when you export/create them in PS. the workflow starts off in AE. You then import the QuickTime into PS and export a GIF. There are lots of options in PS to control the color palette as well as to minimize the filesize.