What extension? You did not tell us. If we knew, someone could provide specific advice. 
First learn how to use the weather extension, make a Project to extract weather information without the BackgroundTasks extension; then learn how to use the BackgroundTasks extension. Then put what you learned together might be a reasonable strategy. Read the documentation for each extension and experiment.
Notes:
You do not have to have an extension to compile weather data from the Web.
- MIT Ai2 crashing - #8 by ABG
- Weather Information Extension
- discussions in the community about using weather information Search results for 'weather' - MIT App Inventor Community