Sounds like you want the configuration from a json instead of the config.js – because then you can change the content.
Or json first and config.js as fallback (and default after that as the last fallback).
So the weather module would have to read it’s config from that json and you can create a module that writes to this json something like weather_source: “location”, and triggers the weather module to reload.

Interesting idea.

EDIT: I found this module while looking for help with something similar:
https://github.com/Jopyth/MMM-Remote-Control

Thanks @Sean. Of course the problem relates to the this reference, which changes depending on the scope where it’s referenced. Thanks for pointing that out!