What did Holmes mean by this comment about the death of the Doctor I cannot say that it is likely to weigh very heavily upon my conscience?

It means that he isn't going to worry about it

The whole quote goes like this:

"And also with the result of causing it to turn upon its master at the other side. Some of the blows of my cane came home, and roused its snakish temper, so that it flew upon the first person it saw. In this way I am no doubt indirectly responsible for Dr. Grimesby Roylott's death, and I cannot say that it is likely to weigh very heavily upon my conscience."