Answer:
When Victor talks about "this deadly weight yet hanging round my neck and bowing me to the ground" , he means he has a great responsibility on which the future of his family depends, but which makes him miserable.
Step-by-step explanation:
Victor clearly feels he has an important decision to make. This decision is totally against his feelings.
Yet, he is scared to break the promise of the marriage with Elizabeth, since that could be crucial for the future of his family.
The words he is using affects the tone at this point of the story, letting the reader know how disconsolate he is.
His idea of this marriage it's totally devastating.
He declares : “To me the idea of an immediate union with my Elizabeth was one of horror and dismay”. The tone with which he expresses the meaning of his marriage is inconsolable, he clearly doesn’t want to do it.
But also, he says : “I was bound by a solemn promise which I had not yet fulfilled and dared not break, or if I did, what manifold miseries might not impend over me and my devoted family” , and here, it can be seen how committed he is with his family. He is attached to a promise that will make him unhappy for the rest of his life, just to save his family future.