Learn Hardcore Icelandic: Okkur líkar veðrið í dag.

Because að líka is used “impersonally”: the experiencer of liking gets dative case. Okkur is the dative of við (we). The thing liked, veðrið, is the grammatical subject in nominative and controls agreement on the verb. Literal idea: “To us pleases the weather today.”

Why is the verb líkar singular when okkur is plural?

The verb agrees with the nominative subject (veðrið, singular), not with the dative experiencer. If the liked thing is plural, the verb is plural: Okkur líka bílarnir (We like the cars).

What case is veðrið, and why the definite ending -ið?

Veðrið is nominative singular with the suffixed definite article (-ið). With líka, the thing liked is in nominative because it’s the subject. The definite is natural here because you mean the specific weather today; bare veður usually means “weather” in general.

Can I say Okkur líkar við veðrið í dag?

Grammatically possible, but líka við is most common with people and often feels more “personal” (be fond of). For neutral liking of things/situations, Icelanders typically use mér/okkur líkar X without við. For people: Mér líkar vel við hana (I like her).