I think this might be Century Rain by Alastair Reynolds. However I'm a bit hesitant because this is an alternate Earth novel and the weather control is only a bit of background and not the main thrust of the novel. However the details do match your description.
In chapter 28 there is a discussion about the weather catastrophe that happened on one of the alternate Earths:
It was late July twenty seventy-seven,” Auger said. “For the last couple of years, we’d been busy releasing tiny machines into the environment in an attempt to fix the climate. The planet had been heating up for more than a century, as we spewed crap into the atmosphere. The oceans were screwed up. Sea levels were rising, flooding coastal town and cities. There were freak storms. Some places got colder. Some places got hotter. Some places just got…strange. Really strange. And that was when some coalition of dickheads had the idea that we ought to try squirting some intelligence into the weather system. ‘Smart weather,’ they called it.”
The smart weather control goes wrong:
“It was never going to work. Late in twenty seventy-six there were rumours—unconfirmed reports—of some weather patterns refusing to follow orders. Ocean circulation events no one could turn off. Clouds that wouldn’t disperse, no matter what you did to them. A persistent obscene symbol off the Bay of Biscay that had to be airbrushed out of every satellite image. It was clear—even though no one was admitting it—that some of the machines had evolved a little too far. They were more interested in their own self-preservation than obeying sequenced shutdown-and-disassemble commands. So you know what the coalition of dickheads did, for an encore?”
“They came up with some even cleverer, slyer machines and said they’d sort out the first wave. And so they were given authorisation to inject these into the environment as well. Trouble is, they only made things worse."
I don't recall anything about humans merging with the rogue nanites. However the surviving humans split into two groups, the Slashers and the Threshers, and the Slashers do use nanotechnology to enhance their bodies. However this isn't related to the rogue weather control nanites.