The Weather app got quite the facelift in iOS 7 and some of the ways you perform certain actions have changed. One of those is how to rearrange all the locations you have inside the Weather app. Here's how:
Launch the Weather app from the Home screen of your iPhone.
In the bottom right hand corner, tap on the list view icon.
Now tap and hold on the weather location you'd like to move up or down in the list.
Drag it to the position you'd like it to be in and then release your finger.
That's it! The Weather app will now remember the new order. Repeat this process for each item you'd like to move up or down in the list. To return to the detailed view of any location, just tap on it.