A simple search has not revealed any extensions called 'Weather Extension'. Who wrote it? Is it this one [Broken it no longer works. Use a weather api instead] Weather Mate ☁ [free]
Have you experimented with your weather extension without the Background Tasks Extension? If not, do so and tell us if it is working for your Android to extract the data you want. You need to learn to use the weather extension (or learn to use a weather api with Blocks ) before you have any chance to use it in the Background (which may or may not be possible). At the moment we do not know what extension you are using and what you have tried. 