There are two different weather options in Microsoft Flight Simulator that you should be aware of. The main one is the live weather option. This is available in data options and will set your weather based on real-time information to know where you are in the game. This setting can be turned on or off in data settings.
When disabled, the in-game weather defaults to local settings, with no live updates. When the live weather feature is enabled, it means that if you're flying over the Atlantic and a storm suddenly sets in in the real world, the same will happen in-game.
You can, however, manually change the weather as you wish. To do this, you will have to go to the Weather tab in the menu that is at the top of the screen. The penultimate option is Weather, and it will let you set a variety of different variables, or choose from presets in the top menu.
You can set cloud cover at different altitudes, time of day, day of year, temperature and precipitation levels, and likelihood of lighting or other weather effects. If you want to give yourself an extra challenge, you can even create wind layers at different altitudes.
This is a very useful feature for people who want to take screenshots of the game, because you can really play around with how the scene looks to take pictures.