I don't know how, but I've made only one weather tile for specific place disappear and there's no option to pin it to start menu again.
What I can choose from is this while others have those. There's no tile for this location pinned at the moment.
start-menutilesweatherwindowswindows 10
Best Answer
If you want to pin or repin an app then click or tap the “All apps” button, long-press or right-click the app you want, and select “Pin to Start”.