Both are amusingly over-complicated.

You don't need a database, just an in-memory cache. All you're storing is recent weather info, which you get from an external server. Caching is just to prevent hitting the external server too hard.

Then the program becomes a single-file executable, which means you can get rid of Docker.

If you set this up to run under FCGI, it can run on some $5/month shared hosting account.