Weather needs to be on in Location Services to show in Notification Center..been that way since the first beta of iOS 7.
I had the same problem then I think I solved it. Of course you need to have location services on, and you probably need background refresh on. But you ALSO need to have Wi-Fi on, at least in my case. Turning on wi-fi helps the phone pinpoint your exact location and therefore providing you a precise current temperature. Try it. (I haven't tested it myself, but I imagine the phone just needs to be able to see wifi networks, you don't need to be ON the networks.)