Learn Swedish: Med tanke på vädret stannar vi hemma. - Considering the weather, we are staying home.

Yes, it literally translates to 'with thought on.' It is the most natural way to say 'considering,' 'given,' or 'bearing in mind' in Swedish when you are basing a decision or opinion on a specific fact or situation.

Why is the word order stannar vi instead of vi stannar?

This is the Swedish V2 (verb-second) rule in action. The entire introductory phrase Med tanke på vädret acts as the first block of information. Because the main verb must take the second position in the sentence, stannar is placed immediately after that phrase, pushing the subject vi to the third position.

Why is hemma used here rather than hem?

Swedish makes a strict distinction between being in a location and moving towards a destination. Because the verb stannar (stay) implies being in a static location with no movement, you must use the location form hemma. You only use hem when there is directional motion toward the home, like in vi går hem.

Would it be correct to add kvar and say stannar vi kvar hemma?