The piece of evidence that would most likely weaken the hypothesis that humans and chimpanzees share a more recent common ancestor compared to gorillas is:
Amino acid analysis of the cytochrome c protein shows significant differences in the sequence of amino acids between humans and gorillas.
This evidence suggests that there may be a greater evolutionary distance between humans and gorillas than between humans and chimpanzees, potentially indicating that the common ancestor of humans and chimpanzees may not be as recent as currently thought. Therefore, it challenges the relative closeness of the relationship proposed in the cladogram.