I have the TM-D710GA so I'm not sure if you have this model or a previous version.
I have one of the panel PF-keys (just below display, to the right) programmed as a 1-touch Weather Channel.
Go into the Menu (press F, then push in the rotary dial), rotate dial to select the AUX group (push in dial), then rotate dial again to menu # 906 or 907 (Panel PF-1 or PF-2). Push the rotary dial in to edit the PF-key, then rotate the dial to select Wx. Ch. Press the key under the display labeled ESC and it's all set.
Whenever you push the PF key that you set for the Weather Channel, you'll get channel-1 by default. Rotate the rotary dial to select the station that you want. When you're done listening tot he channel, press the MR key to the left of the display.