It seems like a lot of people here use Amazing Weather, which is a great app, but I'm partial to Weather Flow. Both of them follow you and update your current location on the live tile, but keep in mind that the tiles only update at a minimum of every 30 minutes (which is an OS limitation, not a fault of the apps), so if you're traveling it won't update for every city you go through, unless you manually update it yourself. Wherever you are when that 30 minute update occurs is where the tile will show you to be for the next 30 minutes.