Caution: a very large project, may cause trouble to your browser.
Snap uses "image/png" as the default format for storing images in the project. The new Web format, "webp" has a much better compression ratio and acceptable compatibility. This change should be fully transparent for users.
Edit: The compatibility table makes this proposal obsolete, as it does not work in Safari. As a loose compression, "image/jpeg" has much better compatibility.
Summary
To get some estimation, I created a project with ~70 large costumes from an image hosting site. The nominal project size is ~16MB and cannot be saved to the cloud. But I instructed Snap! to store costumes as "image/webp". The project size is now 2.6MB and can be saved to the cloud or exported.
My idea is that Snap! should use GZIP to compress the media into way smaller sizes. That way, both images and sounds are smaller without having to change any file formats?
Dedicated encoding/compression schemes do a much better job for their intended purpose, i.e., PNG/WEBP/JPG for images, PCM/Vorbis for sounds, than the generic ones (GZIP).