How, then, can I predict the weather just as accurately (which is really only up to 72 hours at the absolute maximum, the rest is super low probability) with just three of my own miniature weather stations, a python app I wrote, and a few college-level meteorology courses from nearly a decade ago?

I am not controlling the weather, nor do I use any external weather data beyond my miniature station, yet my predictions are often just as accurate (sometimes more-so, but not consistently) than the weather channel's forecasts.