There are several textual clues that help to determine that both the Capulet and Montague families are wealthy, noble, and even ancient families of Verona.
We see the first clue in the Prologue, which opens describing the families with the line, "Two households, both alike in dignity." In this context, the word "dignity" can be translated to refer to "elevated rank, office," or "station" ("Dignity," Dictionary.com). Therefore, we know from this one word that both families have high social status, and they are most likely nobility.
The second line in the Prologue also informs us that both are ancient families as well: "From ancient grudge break to new mutiny." Since their "grudge," or feud, is "ancient," we also know that the two families are as equally ancient as the feud. Their ancient family history can also serve to attest that they are prominent families that are socially high ranking, possibly even wealthy.
Another form of textual evidence proving that the families are of noble birth is the fact that both wives are addressed as Lady Capulet and Lady Montague. If they are both Ladies by marriage, then naturally they're husbands are both Lords.
A fourth piece of textual evidence is that in the opening scene, the stage direction Shakespeare uses to bring Capulet on to the set is, "Enter Old Capulet in his gown, and his Wife" (I.i.71). The term "gown" can only refer to his courtier's gown, proving his wealth, noble lineage, and prominent social status. Similarly, another textual clue that helps to depict Capulet's status is the fact that County Paris has asked for his daughter's hand in marriage. County is another name for a Count, which has a much higher noble rank than a Lord. Lord Capulet would only consider allowing a man of equal or higher status marry his daughter. County Paris also gives us textual evidence that both families are considered to be of high rank when he assures Capulet of his status by saying, "Of honourable reckoning are you both" (I.2.4). The phrase "honourable reckoning" can be translated to mean honorable status.
Finally, we also learn from Romeo at Mercutio's death that Prince Escalusis actually a relation, probably by marriage, of Mercutio's. We see this in Romeo's lines,
This gentleman, the prince's near ally,
My very friend, hath got his mortal hurt. (III.1.110)
The term "ally" can refer to a unity by marriage ("ally," Dictionary.com). Hence, Prince Escalus was related to Mercutio. If Romeo is close friends with Mercutio, a relation of the prince, then that also serves to prove that the Montagues were indeed wealthy courtiers.
The play opens with a statement that the Montagues and Capulets are two households "alike in dignity" immediately telling the reader that these two families are of a similar class. Evidence of their wealth can be found in their practices. The Capulets, for example, throw lavish parties (like the one that Romeo crashed when meeting Juliet). Also, the fact that Juliet's parents are trying to arrange a marriage with Paris is also an indication of their wealth as this practice was most common in families that were of higher social classes.