어깨가 무거워요 · 어깨가 무거웠어요 (ㅂ irregular)
to feel a heavy responsibility, to feel the pressure
Example
새로 팀장이 되니까 어깨가 무거워요.
Now that I'm the new team leader, I feel the weight of responsibility.
Word parts
Responsibility pictured as a load on your shoulders, much like in English.