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 a certain protein shows significant differences in the sequence of amino acids between humans and gorillas.
This suggests that humans and gorillas may be more closely related than previously thought, which directly contradicts the idea that humans and chimpanzees share a more recent common ancestor. If there are significant differences between humans and gorillas in terms of protein structure and function, it could imply that the common ancestry model needs to be reconsidered.