The piece of evidence that would most likely weaken the hypothesis that humans and chimpanzees have 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 are greater differences in protein sequences between humans and gorillas than between humans and chimpanzees. If humans and gorillas are found to be significantly different at the molecular level, it could imply that the divergence between humans and gorillas occurred earlier than previously thought, thereby weakening the idea that humans and chimpanzees share a more recent common ancestor compared to gorillas.