Just for reference, the trip from St. Bart’s to 221B and back takes about half an hour.
I think the first part of your question, about the night-to-day transition, is pretty well covered by the story in the episode.
When Sherlock and John were at Kitty Riley’s, it was night.
Then they each went off and did their own things, and it was still night when John arrived at the lab. John helped Sherlock figure out the key code thing, at which point Sherlock texted Jim to meet him on the roof.
Then Sherlock and John hung around the lab until early morning. It was starting to get light outside, and John had fallen asleep.
John got the call about Mrs. Hudson, and then Sherlock got the text letting him know Jim was waiting.
By the time Sherlock arrived on the roof, it was bright out. Even if the lighting transition from the last exterior shot was a little dramatic, I think there’s nothing to it story-wise except we were meant to understand the sun was now up. (Jim probably waited until that point to show up because a public suicide is much better in the light of day.)
As for the other part of your question, about the weather… Yes, I think it is all very much down to the filming.
It did get cloudier during parts of the roof scene.
But it takes hours to film that kind of thing. There’s not a lot they could do to stop the clouds from moving across the sky. If you skim through Sherlock and Jim’s conversation and only watch the clouds, you’ll see that they aren’t at all consistent from shot to shot.
Then there was the sky later when Sherlock was standing on the edge of the roof.
Also very cloudy. But that part was filmed on a different day and a different roof than the rest. And we know they were coping with getting the filming done despite bad weather when they shot that part.
[Behind-the-scenes pic via dailymail.co.uk]
So again, down to the filming. A boring answer, perhaps, but almost inescapably true.
At least until the truth about Moffat’s weather machine is revealed.