Weather app window glitched upon opening.

You may try this first

1 - Restart in Safe Mode. This will perform a Disk Repair, clear cache files and only load Apple Software, extensions and fonts. The boot up will be slow and can take some time - Normal.

2 - Safe Mode will also eliminate Third Party Software, extensions and drivers from loading. It will only load the Minimum amount of Core Apple Processes to allow the the computer to function at a reduced Level of Performance 

3 - Does the issue present in this mode ?

4 - Sometimes a Safe Boot followed by a Normal Boot will just put things right.

5 - Still having issues, then try with the Application completely closed.

6 - Hold the SHIFT key and Launch the Weather application.

7 - This is a Safe Launch of the Application

No, I am not a ChatBot if this maybe of concern

Alric3107 wrote:

It does not change anything though... I am just interested to know if this is the problem of the Software and not just for my Mac. Does anyone else experience this? Thank you!

On 3 different Apple Computers, all running Ventura 13.5.1 , the latest and greatest stable version of Ventura .

No issues here

If your computer issue is reproducible on a regular basis and Apple can also reproduce it on their side.

Then perhaps Apple needs to be informed of this issue

Then I have a few suggestions ;

1 - Get Support Choose a product and we’ll find you the best solution.Start now and open an Apple Support Ticket as they are Apple Employees to deal will these types of issues . 

2 - Product Feedback - Apple and make it known to Apple regarding this ongoing issue 

In System Settings > Desktop & Dock > Windows, makes sure "Close windows when quitting an application" is disabled. Also, don't click the red close button before quitting Weather.

You're welcome. Actually, as far as Weather, you can click the red close button.

It describes what it does under the setting. But basically with it disabled, most apps will reopen with the same windows that were open when you quit them.