"Weather" covers a lot of sins. You will find that a lot of what gets called (and allowed to be called by the FAA/DOT) "weather" is, as you point out, not really weather, but operational choices.
When a storm hits a city, yes, the first plane that had to wait to take off from the airport can be said to be delayed by weather. Every other plane waiting in line behind that plane, delayed, or because they weren't able to get to that city from other destinations because they run an overly tight schedule, is due to operational choices by the airline.
Some airlines have hubs in places where snow is handled ok. Some don't. Others have them in places that have frequent thunderstorms. Some airlines operate in Hawaii and never have delays.
JetBlue used to fly A321s across the country and in the winter, strong winds would force them to stop in Kansas to refuel. That's "weather" but also the airline's choices about how to operate.
I don't think you'll ever find the FAA/DOT is going to "root cause" what weather means to airlines to be able to blame them for operational / strategic choices. It would be like the police writing up your car accident report and saying that the reason you had a fender bender was because you chose to live so far away from work.
Thus, choose your airlines and roll your dice accordingly for when you want to get where you want to be.