Circles is probably a widget. Check in your widgets to make sure you have it there. Then you can always get it back.
If it's not a widget, check in your app drawer to see if it's an app. What's on the homescreen is just a shortcut to the apps, so deleting them from the homescreen doesn't delete the app.
If you want to go back, if it's a widget, long-press a blank spot on the homescreen, select widgets, then select the one you want. It'll appear on the current homescreen. (Scroll to the one you want it on first, so you don't have to drag it across screens to get it where you want it.)
If it's an app, scroll to the homescreen you want it on, go to the app drawer, long-press the app and drag it to the homescreen.
If it's not an app, shortcut or widget, get back to us. I use the Accuweather app and widget (because I've used their add-on in my browser for years, so I know how to handle Accuweather, but I'm not familiar with "Circles" - that's got to be a Droid thing. Accuweather itself is a widget for the homescreen and an app for full forecasts, weather alerts, etc. And it can be set to Imperial or Metric (F/C, miles/km, etc.), time and date format, what temp range you consider comfortable, all sorts of things. It does come with ads unless you pay for it, but I never noticed them until I just checked the settings to see what's changeable and noticed a "disble ads" choice, which is a link to the paid version. (Now that I look, there's an ad at the bottom of the full app - hard to notice. Nothing on the widget.)