People are different. Not everyone uses weather as an entry point to other topics. Some talk about weather and just this, when in the elevator, with no intention of going forward.
This is, I believe, to cover discomfort coming from silence and such conversations, while not completely pointless, often have little value. They would talk about just anything, to combat this feeling. Weather is a good topic because most people can relate and it is rarely annoying.
I would say that both intro- and extroverts can act like this but conversations started by introverts tend to be more awkward. I think that lonely people are more likely to start valuable conversations.