게 계시다

stay a certain way (honorific)

계시다 is the honorific of 있다, used about someone you are showing respect to, and the "-게" adverb in front says what state they are in: 건강하게 계시다 stay healthy, 따뜻하게 계시다 stay warm, 심드렁하게 계시다 sit there unimpressed. Most lines are wishes and polite check-ins — I hope you stay healthy another ten years, I wonder how you're all keeping, how are you managing at 3,300 metres? Use it about other people, never about yourself.

Register: polite, honorific