Well, the wedding is easy:
How do you know [couple]?
Have you come far?
I often use 'have you come far?' in many situations, as you usually then say 'Oh, that's a lovely place / I know X who lives there' and if need be 'Have you lived there long?'
Although I agree in principle with esspee, there are some shy people who answer the question and and don't give you anything much to carry on with. I find that some people will often talk more if they feel you have shared something.
Weather is safe, and if I feel I need to 'keep going' a bit, I'll say something like ' And we're hoping it will be this nice / nicer than this next week, we're going to a festival / next month when our friends are having a garden party'. This usually lead to some sharing about what people are doing.
If they say something about a topic you don't know much about, you can say 'how do you find that works out? are you glad you did that? do you find that uncomfortable / pleasant / whatever'.
And don't be afraid to tell a funny family story (edited for blushes) which invites their similar anecdotes.
And in the end, if they are really not going to be drawn, just accept that is how some people are, and see someone across the room you really need to talk to.
And if it all goes belly-up, then store it your treasure chest of anecdotes - like the person I met who on hearing I had been a NHS nurse all my working life, proceeded to instruct me on how mistaken the concept of a socialised health service was!
Oh, and it's not 'silly', it's what people who care about others' comfort do.