Explain why oxygen consumption varies with body weight.?

Our body is made up of about 35 trillion cells, each of which requires maintenance, hence supply of oxygen.

Since the size of cells do not generally vary from person to person, we can reasonably assume that the number of cells vary almost linearly with body weight.

We can also reasonably assume that the oxygen requirement vary directly with the number of cells.

All this is to say is that oxygen consumption/requirement varies directly with the number of cells in our body, hence body weight.