Window size, returns to small after boot-up...

1 - try holding down the Option key while resizing the window to your specs. Then reboot and check again.

2 - if still a problem boot into Safe Mode by booting with the Shift key held down and check there to see if the problem persists.  Reboot normally and test again.

NOTE: Safe Mode boot can take up to 10 minutes as it's doing the following; 

• Verifies your startup disk and attempts to repair directory issues, if needed

• Loads only required kernel extensions (prevents 3rd party kernel/extensions from loading)

• Prevents Startup Items and Login Items from opening automatically

• Disables user-installed fonts 

• Deletes font caches, kernel cache, and other system cache files

In one or two previous versions of macOS, the following "trick" solved your problem. Perhaps you can try if it works in Big Sur also:

1. Open a new Finder window.
2. Resize it to your liking.
3. Press Command+N to open a second, identical Finder window.
4. The second Finder window will be the same size as the first, resized one.
5. Cross your fingers, restart your Mac, and see if you're lucky.

Make sure you have read and write permission on the Home folder.