I did not mean to imply that NOAA's annual budget gets us weather data for all time. I specifically meant that the value of NOAA's data and services, each year, well exceeds the annual cost to taxpayers. (One could argue that some of the money spent on research - developing weather models - is a one-time cost, because now that we have them they don't need to be re-invented every time we use them.)
Taxpayers have historically been willing to pay the costs for all the new data, but they have cut the budgets going forward, so obviously taxpayers are not willing to pay anymore for what they are getting
To be pedantic: taxpayers didn't cut the budget, their representatives in Congress did. It is not at all obvious to me that this is what taxpayers want. I suspect that if you were to ask taxpayers across the country, and present them with the numbers, the majority would say that NOAA's budget is not actually that large, and that cuts to the premier weather service in the country seems like a bad idea. In an ideal world, the representatives would be expressing the will of their constituents in each and every vote. In practice, that is only sometimes the case, because democracy is the worst form of government (except for all the others). And at the moment, Congress appears to be particularly pliant to the whims and demands of the Executive, with a particular animus against science and expertise, even when Congress ought to know how penny-wise-and-pound-foolish it is.