"I regard you with an indifference closely bordering on aversion"

This quote by Robert Louis Stevenson suggests that the speaker has a negative opinion of the person they are resolving. The speaker is revealing that they see the person with a lack of interest, and that this lack of interest is close to a sensation of dislike or repulsion. This quote recommends that the speaker has a strong negative viewpoint of the person they are addressing, and that they are not thinking about forming a favorable relationship with them. It is possible that the speaker has actually had a negative experience with the person in the past, or that they simply do not like them for some other reason. Whatever the cause, the speaker is revealing that they have a strong unfavorable opinion of the individual they are addressing.