The expression "What a weight off my shoulders!" is an idiomatic way of expressing relief after a burden, worry, or responsibility has been removed or resolved. It refers to the feeling of being free from something that was weighing heavily on a person's mind or emotions.
This saying originates from the concept of carrying a heavy load on one's shoulders and the relief felt when that load is finally removed. In conversation, it's often used to describe a sense of relief, relaxation, or freedom after dealing with a challenging or stressful situation.
For example:
I finally finished my thesis paper. What a weight off my shoulders!
Completing that project before the deadline was such a weight off my shoulders.
Finding a new job after months of searching was truly a weight off my shoulders.
I was so relieved when I found my lost dog; it felt like a weight was lifted off my shoulders.