Round characters feel like real flesh and blood to the reader. They are characterized as genuine people with a range of emotions. Round characters develop and change as the story progresses, either emotionally or through some sort of revelation. Since Benvolio is a minor character, his changes are less obvious, but he certainly is a realistic person and a round character. Benvolio is, for the most part, one of the only rational characters in the play. He is the one that most wants peace. For this reason, we don't really see him changing his perspective throughout the play, but we do see him developing different emotions. We even see him acting less sensibly at times.
We see evidence that Benvolio is the sensible peacemaker in the very first scene. When Benvolio first comes on stage, the first thing he tries to do is stop the Montague and Capulet servants from fighting; however, Tybalt misinterprets Benvolio's actions, thinking Benvolio has started a fight with the servants, and makes the fight even worse, turning it into a whole city brawl. Benvolio's stance on wanting peace does not change throughout the play; it is even evident in the very last scene Benvolio is in, the scene in which both Mercutio and Tybalt are killed. Like the first scene, Benvolio is the one who is called upon to explain what has just happened. Benvolio's desires for peace help him to see that Romeo was trying to pacify Tybalt when everything simply got out of hand, as he explains to Prince Escalus in the lines, "Romeo, that spoke him fair, bid him bethink / How nice the quarrel was, and urg'd withal / Your high displeasure" (III.i.157-159). Hence, Benvolio shows through his recognition of Romeo's actions just how much he values peace, which is not a perspective of his that changes throughout the play.
However, Benvolio's emotions do change throughout. When we first see Benvolio with Romeo, Benvolio is feeling very sympathetic for his friend. In fact, Benvolio feels rather grieved to see his friend so heartbroken, as we see when Romeo asks Benvolio if he is laughing at Romeo, and Benvolio replies, "No, coz, I rather weep" (I.i.182). Benvolio becomes determined to help Romeo out of his misery and distract him with other women. Hence, in the scene in which he and Mercutio try to persuade Romeo to crash the ball, Benvolio's mood is very cheerful. Plus, when we see Benvolio again in Act 3, Scene 1, Benvolio is feeling very apprehensive and warns Mercutio to get off the street.
Another way in which we see Benvolio changing as a character is that, as the sensible peacemaker, there are actually times when his character is less sensible than other times. The best example of Benvolio acting without sense is when he decides to persuade Romeo to go to the ball. True, Benvolio had Romeo's needs in mind. Since Rosaline would be at the ball as a relation of Capulets, being at the ball would give Romeo a chance to see how Rosaline compares to other women in Verona. Seeing Rosaline in perspective would help Romeo forget about her and move on. However, Benvolio somehow manages to forget that going to the enemy's house would be dangerous and most certainly lead to grave consequences. Therefore, convincing Romeo to go to the ball is one moment in which Benvolio acts with less sense than he normally does.