Student or Learner
1) I am glad that i don't have to look after him for the weekend, at least now i can take some responsibilities/burden off my shoulder.
2) By not having to take care of him you can lift some responsibilities off your shoulder.
#1: I think it should be "shoulders" and it needs a semicolon instead of a comma: "I am glad that I don't have to look after him for the weekend; at least now I can take some responsibilities off my shoulders.
#2: Is correct grammatically, but still sounds very awkward to my ears.
*** Not a teacher, but a native Engllish speaker ***