Puns in Shakespeare's tragedies, such as Romeo and Juliet, serve the purpose of lightening the dark mood with humor to keep his audience drawn in and engaged.
In Romeo and Juliet, a few of the characters act as comic relief by making puns.
In the opening scene, Capulet's servants make several puns in their dialogue. Sampson uses the phrase "carry coals" to refer to humiliation. The act of carrying coals was the task that the chambermaid performed, the least significant household servant. Hence, carrying coals was seen as an insulting and demeaning task (Romeo and Juliet, eNotes). Therefore, when Sampson says to Gregory, "On my word, we'll not carry coals," he means to say that he will not allow themselves to be humiliated by the Montagues, making a pun out of the word "coals," which is referring both to literal coals and to humiliation. Gregory twists Sampson's words into a further pun in his reply, "No, for then we should be colliers." The term colliers, pronounced "coalers," refers not to chambermaids, but to "coal miners," forming another pun out of the word "coals." (eNotes).
The character Mercutio is also well known to make puns. In Act I, Scene 4, when Romeo says he feels uneasy about crashing the Capulet's feast due to a dream he had, Mercutio states, "That dreamers often lie," creating a pun with the word lie. Mercutio is using "lie" to refer both to sleepers lying down and to untruths. Hence, Romeo responds with, "In bed asleep, while they do dream things true," meaning, they lie down while being in "bed asleep," and they dream about things that are "true."
Earlier in this same scene, Romeo makes a pun of his own when he says,
Give me a torch: I am not for this ambling;
Being but heavy, I will bear the light.
Romeo is making a pun out of the word light, using it to refer both to literal light from the flame of a "torch" and to lightness of weight. Romeo is saying that since he feels sorrowful, or heavy hearted, he will carry the torch, thereby carrying the light, and becoming lighter in emotion.