When searching for “weather” without a city appended, the widget is being for a city which seems to be taken from a geoip database. However, these databases can be quite inaccurate at times.
I see two possibilities to circumvent said problem
1) Have an Option “Hometown” where the user can set up, what town to use when no further arguments are given
2) Use the last explicitly searched for city, assuming the user will continue to search for this place
I'm not sure which option of these I like better... Maybe both and toggleable?