'소중히 여기다' means 'to cherish/treasure/value something', and '소중히 여기는' is a form of adverb+adjective. 소중히/소중하게(adverb) = precious, valuable, important 여기다(verb)= regard, consider, think '소중하게 여기다'= regard/consider something as valuable/important Example) It is one of my most treasured pieces. = 그것은 내가 가장 소중히 여기는 작품들 중의 하나이다. That's why my family members cherish me = 그것이 나의 가족 구성원들이 나를 소중히 여기는 이유이다. Example)

I'm not 100% sure, but I think it means to treasure/value something. If there is an object attached to that phrase, it is asking you to care for that thing. Here is an example I pulled off of Naver. 귀를 소중히 여겨요. treasure these ears. 듣기 채널 썸네일MYSTIC ENTERTAINMENT 장재인의 가을룩 추천