In their paper on Image Pyramids, Burt and Adelson state the following about pyramid generation.
An additional constraint is called equal contribution. This stipulates that all nodes at a particular level must contribute the same total weight($=\frac{1}{4}$) to nodes at the next higher level. Let $\hat{w}(0)=a$,$\hat{w}(-1)=\hat{w}(1)=b$,$\hat{w}(-2)=\hat{w}(2)=c$. In this case, equal contribution requires that $a+2c = 2b$.
How is this weight condition derived and why is the weight $\frac{1}{4}$? For a larger context of the question, the screenshot of the relevant section in the paper can be seen below
