Why does Romeo use iambic pentameter?

Romeo is a member of the aristocracy, and thus has more formal language than members of the lower class (the servants, for example). Shakespeare regularly used this convention to further distinguish royalty and aristocrats from the common folk (obviously, they were already distinguished by their costumes to some extent).

Romeo primarily uses heroic couplets, though, which is unusual for Shakespeare, who usually satisfied himself with blank verse. (Heroic couplets are two lines of iambic pentameter that rhyme; blank verse is iambic pentameter that doesn't rhyme.) Just like each scene is opened with a sonnet--a poetry form used primarily for pastoral and love themes--heroic couplets were primarily used for heroes.

Iambic pentameter, by the way, is said to have been the meter of choice because it so closely mimics the rhythm and length of a standard English sentence. Putting dialogue into iambic pentameter gave the lines a pleasing rhythm, making them more memorable, and had the added benefit of making them easier for actors to memorize.