I work in this space. The load on private APIs -- and the management costs in general of reselling government data -- are utterly dwarfed by the upstream costs borne by the government.
The public __already__ pays for Google, The Weather Company, Apple, and really __everybody__ -- down to your local weather person and surf report -- to use weather data on a massive scale.
Government weather data underpins huge chunks of our modern, globalized economy. It should absolutely be better funded and even allowed to directly distribute data to the public and industry. NOAA and NASA et al could be given 10x their current allocation of tax money and you and I would still be getting a great deal.