>... to move away from a heavyweight distro like fedora or ubuntu, to something like alpine or even more minimalistic.
The distro package management is one of the biggest reasons why people still stick with heavyweight distros like Ubuntu.
This is why DockerSlim  was created (at one of the Docker hack days, by the way :-)) It lets you use heavyweight distros as-is eliminating everything you don't need. You get the best of both worlds where you don't have to change your process and you still get small images (7, 10, 20 and even 30 times smaller than the original).
 - http://dockersl.im
It is safe for use in production :)
And if you are using 3rd party Docker images Alpine won't help :)