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I guess if you wanna do it that way then I have a better way. Download the tweak called WebSpot which replaces spotlight with a browser and then go to Safari and google "weather your location" (e.g. I would google weather dublin) and then copy the link in the url and paste it in the WebSpot settings. Here's a screenshot. This way you'll always have it there without having to type or do anything and you can have it to auto refresh every time you open the spotlight page.

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My guess (while I'm not a developer), would be that it requires Apple to sign with Google to do it, because wouldn't Google need to have some special setups to relay specific information like that to the widget?
 
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