Is it possible to get each user to register as "developer" and use his own key? Then, due to low number of calls from each "developer-user" to API, each key will be free-of-charge - developer has to pay only when number of calls to API becomes too large.

It may be absurd, because it gives the weather-provider email-and-such of each user. Hence, if you prefer to use a key provided by other person (aka developer of the app), be prepared to pay to the developer as the developer will have to pay to weather-provider for huge number of calls to API going through him.

Thank you. Best wishes.