When you say something is a 'weight off your mind' or a 'weight off your shoulders' it means something you have been worrying about or responsible for is no longer a concern. This is a casual phrase that can be used in both social and professional contexts. Similar in meaning to 'a relief'.

1. Finally paying off my loan to the bank was a big weight off my shoulders. That had been hanging over me for a long time.
2. I met my best friend for coffee yesterday. Sitting down and talking with her helped me get a weight off my mind. 

1. It's a real weight off my mind to know that the deal has now been signed. I had been worried about it falling through for weeks!