This seems to be due to the fact that the translated phrases are uppercase... partly.
If we look at the German translations for the weather widget:
Her the weather is translated to Wetter (upper case W). Now, searching for Wetterwith both upper case (left) and lower case (right) W, doesn't yield any weather widget:
Now, searching wird es regnen (translated all lower case) with every word capitalized (left) vs not (right), both yields the widget:
If we look at french, and their translations of the phrases to trigger the dictionary:
Here searching for, for example, definir water with the dcapitalized (left) and not (right). In the translation, it's uppercase.
Searching for sens water (this translation is not upper case), we get the opposite result:
More phrases are also translated with the first letter upper case, but I don't think I need to list them here.
Conclusion
Sometimes the widget doesn't show if the translation of the phrase to show the widget is capitalized. With German, that isn't the case though. This also kind of ties into a suggestion I have which is that Kagi should be much smarter when showing the widget (fx, in french, météo and meteoshould both show the weather widget, which doesn't happen currently) if the letters are capitalized/accented
