What is "large", approximately? Tens or hundreds of megabytes or gigabytes?
Should compress down nicely. APK files are compressed. Is APK still too large, even after this?
Bear in mind that HTTP works for any type of file, not just HTML, TXT, etc.
If it is CSV data and you're not worried about user download quota or cost then... Google Docs has a public download link feature delivers a Sheet in CSV or TSV format. Works great. But it's in uncompressed cleartext.
Another free-hosting way of doing it would be to compress the data, and then store it as pixel data in a lossless image format, and host that on a picture sharing site. If site has a picture file size limit, then can store as multiple picture files ie bigdata1.png bigdata2.png bigdata3.png... or maybe holiday1.png holiday2.png holiday3.png... to keep things innocuous
GitHub projects let you store files, and I'm pretty sure they can be directly linked to and download using HTTP.
Dumb question, but just in case: data is the same for all users, right?