The headers are missing on the live site when requesting “/” and “/index.html”, but interestingly they are present when requesting “/test.html”.
I noticed a header fly-cache-status: HIT on “/”. Are you using [[statics]] by any chance? As the docs say, you can’t set headers with that. See also: Removing [statics] from fly.toml has no effect.
You could try to confirm that the issue is with the Fly configuration and not with nginx by starting an SSH session and running wget -O /dev/null -S http://localhost:3000 to view the response headers (probably need to install wget first using apt-get update and apt-get install wget).