In the context of the play, Romeo is expressing his frustration with the upcoming marriage between Juliet and Paris. He reflects on Paris's physical attractiveness and social standing, but also notes his lack of emotional depth and sincerity. Romeo believes that Paris's face reveals a superficial and shallow nature, unlike his own passionate and genuine love for Juliet.
Therefore, the phrase "Read the volume of young Paris' face" encourages the audience to look beyond physical appearance and consider the deeper qualities of a person before making judgments or forming opinions.