If that doesn't make a difference, go into the application manager/manage applications in your device settings and locate the Play app and then clear the cache for Play.
This should force the Play app to re-query its database for purchases.
If you have multiple Google accounts on your google play, Please redownload the app making sure that you are using the same account that you had used to purchase 1Weather in the Playstore earlier.
If the issue persists, follow these steps.
Open 1Weather>Menu>remove Ads. Now press $1.99 in the dialogue box that appears. If you have only a single google account on your device, this step will typically make google play recognize your purchase.
Would you mind reaching out with the screenshot of your proof of purchase to us at email@example.com if you still face issues