The distinction between planets and moons is, at least somewhat, arbitrary. Some moons have atmospheres, and if they do, they'd also have weather. And then, of course, the atmosphere is the distinguishing factor as to whether they do or not.
It's obvious that the Sun, combined with the atmosphere, is the primary driver of weather and climate. But the *combination* is important. The composition of the atmosphere is as responsible for the weather and temperature, if not more so, than the Sun. As an example, strip away the atmosphere (or at least the greenhouse gases within it), and the Earth's average temperature drops by some 30-odd degrees.
As a general rule of thumb, if you start off by assuming something scientific is simple then you'll quickly be led astray. Things are invariably more complicated than you'd like. Especially in systems as complex as the Earth, when you have to consider interactions between land, sea, and air. Just saying "it's all the Sun", as if that settles the question, is a great way to be certain of being wrong.
There's no personal attack, here. There's no shame in being, at least initially, unable to keep track of scientific developments and the understanding that emerges from them. Science is hard. But it's precisely that hardness that makes the obstinacy of insisting it's so simple such a shame. Learn, research, admit your gaps in understanding, accept your ignorance and strive to reduce it! Have no shame over them. But never make the mistake of thinking that you know better and that there's nothing more for you to learn.