Title says it all.
Huh? The launcher is not 15 gigabytes.
I’m confused as well…
do you have any packs from the marketplace in your library?
Mostly this happens because of your VaultCache -> there all projects that you have downloaded from the marketplace will get stored. So just delete it and you will drop the GB count 
I believe the launcher is around 300MB and UT4 is around3.9GB.
If you have multiple engine version installs… that could also end up being an issue. I have 4.9 and 4.8 installed and they both take up a good bit together. In reality you only need one engine installed unless you have a custom version of it. Once you upgrade a project and mainly the map files, you cannot role back the project once saved in a higher one. Remember that for future reference as a friendly tip!
for me the launcher and only UE4.9.2 together take up 15.2 gb
Have the latest update I BELIEVE by default you have projects in the vault.
Try deleting one and see if the GB count goes down.
~ Jason
that is without project files, the Engine folder alone inside the 4.9 folder is around 13 gb, anyway it’s not a big deal to me but just wanted to tell the OP that it is not just the launcher that takes up those 15 gigs