Who makes the official call? The airline's operations center (see post #2). Might they have incentive to aggressively code as weather? Yes. If you feel that they are in error and want to demand compensation, you can challenge it with customer service, and if necessary as far as the CTA. Introducing a 3rd party into the process to overview every delay in real-time is crazy

As for the cabin crew repeating "weather weather weather"--I think the explanation there is something OTHER than them aggressively helping the company to avoid paying compensation. How was the mood aboard the flight? If many pax were upset, maybe they just wanted to shift the blame somewhere else. Why would the FAs care about your compensation--it doesn't come out of their pockets. I can see them having instructions not to promise the world (in compensation) upon landing, but really what reason is there for them to care what happens after you land? They just want a peaceful flight