The weather widget only seems to display when searching "weather". Various other related terms that probably warrant a forecast (that Google picks up on)
- temperature
- humidity
- forecast
- precipitation
And more human queries such as:
- will it rain
- do i need an umbrella
- wind
- wind speed
I live in a humid location, and often I don't care about the temperature, but the humidity, so that's why I search for it.