What evidence exists in the play of Romeo being frivolous or joking around a lot?
In Act 2, Scene 4, when Romeo sees his friends Mercutio and Benvolio, after having abandoned them the night before to sneak into Juliet's garden, Mercutio gives him a hard time. He and Romeo engage in some witty repartee in which they make a number of sexual references via words with double meanings. This section very much shows Romeo's frivolity and joking nature.
Mercutio is irritated that Romeo blew them off, but Romeo says that he had some important business to attend to, and so he had to risk being discourteous. Mercutio replies, "That’s as much as to say, such a case as yours / constrains a man to bow in the hams" (2.4.23-24). He suggests that Romeo's important business was sexual (that it made him "bow in the hams" = to flex his butt muscles as he would do if he were having sex). Then, when Mercutio claims that he is "the very pink of courtesy," Romeo turns the joke back on him by referring to a "pink flower," by which he means female genitalia. Mercutio acknowledges the joke, and Romeo says, "Why, then is my pump well flowered," meaning that he has had a lot of sex (his "pump" = his penis). This kind of joking, sexual banter, where Romeo and Mercutio attend to one-up each other with puns and double entendres, shows how frivolous Romeo can be.