You can talk about recent weather patterns using the phrase "weather we've been having":

This is a strange bit of weather we've been having.

Nice weather we've been having, isn't it?

You use "have been ___ing" when you're talking about an action or state that is:

• continuing
• recent

Another example of "have been ___ing" is:

I've been working hard on finding a replacement for Abby now that she's left.