Google uses barely any weather data. Perhaps some tornado and wildfire tracking for its datacenters, but that's about it. The vast majority of its potential use comes from Android users, which is... the general public.

And it's not like Google is a charity, you're paying for it either way. The question is: do you want to pay for that weather API via your taxes, or do you want to pay for it via the advertising budget of the products you buy - with Google taking a decent chunk and selling your location data while they are at it?

And it's not like operating a weather API is that hard. You can easily find commercial parties who sell it for less than $1 per million API calls. Assuming you're polling for weather updates every 15 minutes 24/7, that's less than $0.03 of your yearly taxes going towards providing accurate weather information!