If you limit it to "Official" sites and have wifi security enabled I don't think it'll be much of a risk.
For home use I wouldn't bat an eyelid, for a weather station at your desk in a military base, hospital or bank, i'd probably think twice just incase.I looked around but couldn't find a thread for this topic, sorry if I missed it...
I recently found my first tablet. A Samsung Galaxy Tab 7 (SCH-I800). It's ancient, one of the first 7 inch tablets, and was quite spiffy when it was released.
My idea was to set it up as a news/ weather station. Just leave it in the charging dock and let it scroll through news & weather updates via wifi. Nothing too spectacular, but I figured it's better than just tossing it.
My concern is that it might make my home network vulnerable. It's limited to Androi 2.2, Froyo, though it does have Avast anti-virus installed.