The World State seeks to control everything about its citizens and environment. The weather, of course, presents a bit of difficulty. As far as we can tell, the World Controllers haven't figured out how to make the weather, so instead they try to control the perceived environment, through soma and indoctrination. Observe Lenina and Henry's drug trip: "They were inside, here and now – safely inside with the fine weather, the perennially blue sky. […] The depressing stars had travelled quite some way across the heavens. But though the separating screen of the sky – signs had now to a great extent dissolved, the two young people still retained their happy ignorance of the night." Then there's that calming, controlling song that seems to be forever playing in the background: "Skies are blue inside of you, / The weather's always fine."
Of course, the weather is not always fine, and those that recognize as much are those who are able, even for the briefest of moments, to step outside the distorted reality of the World State and look the real world in the stormy face. We're thinking… Bernard and Helmholtz. Look at Bernard's date with Lenina – he takes her to the edge of the water to look at the weather, which "ha[s] taken a change for the worse; a south-westerly wind ha[s] sprung up, the sky [is] cloudy." Interestingly, it is this dreary image that makes Bernard feel "as though [he] were more [himself], […] not just a cell in a social body."
Of course Lenina just switches on the radio, which quite appropriately is playing the "skies are blue inside of you" ditty.
Helmholtz picks up where Bernard left off as far this weather thing goes. Throughout the novel, he's been wanting to write something with the passion of Othello – it's just that all the passionate topics (love, jealousy, hatred, family, age, death) aren't available to him as subject matter. What is it that he can understand that makes him feel, perhaps, as though he, too, is more than "just a cell in a social body"? What's the only intense, violent thing left in the World State?
Um…peanuts? No, the weather. Look at what Helmholtz says at the end of his conversation with Mustapha: "I should like a thoroughly bad climate […]. I believe one would write better if the climate were bad. If there were a lot of wind and storms, for example…"