What about cache?

The media that you use (photos/videos) are converted so that they fit Quik's technical requirements.
Pictures are resized (1024x1024) to be used in the rendering engine. Plus the bitrate of the video is chosen to have a good compromise between video quality and upload time.

Once they're converted we store them so that we don't have to do the conversion again the next time you use them.
Normally the size taken by those converted elements is small, however if your project has many many elements, then it will take more space.

It's important to know also that the songs uploaded from your library are stocked in a cache folder which can be cleaned regularly by the OS to create room on your device. It's something we do not have our hands on.

Another point is that the app itself is big, 100MB, because all the video styles requires lots of graphical assets and the 3D engine is quite heavy as well...

QUIK ANDROID has a clean cache button in the Settings. Be aware, this will delete elements that are being used and you may not be able to duplicate and edit a video.