Hello.
I think,the Weather/News Channel are no longer working,when you turn it completely OFF.
But as long as
your Wii is completely turned off (RED LED) you don't need to be afraid of it and yu do not need to turn the Stand By Mode off.
You receive the Notifications a "little later",as soon as you boot into the Wii System Menu.
Many Homebrew Applications like the USBLoader GX for example can turn the Wii completely off when you leave it.
Thank you.