(Jeanne, I took the liberty of changing "with" to "without" so as not to confuse people :-)
If I'm checking the weather is that a secret?
People have different levels of perceived privacy and security needs. You may not mind, but someone else may not want other people to know for which cities she checks the weather. And in the ever more numerous public WLANs it's easy for other people to snoop on unencrypted traffic. Given how easy it is these days to set up HTTPS, and how little overhead it actually creates, I think this is a good path to take.