I think you might try lightening up a bit if you can. Carpe Diem.
Sometimes instead of asking yourself, "Does this conversation affect my life for the better?" maybe you should just enjoy a moment. Yes weather conversations are as useless as you described and I agree, I hate them as much as you do. But maybe you should try not to over analyze every word that comes out of somebody's mouth and just go with the flow. Make a joke about how extremely bored you are in a way that comes out funny. Express your own personality.
It works for me. I hope you start to enjoy life a little more, somehow.