In this scene, when Romeo first sees Juliet, she is dancing with a knight at her father's feast. Since she is dancing, she is holding the hand of her partner. When Romeo asks a servant who Juliet is, referring to her as "enrich[ing] the hand" of a knight, he is seeing Juliet hold hands with the knight and thinking of how blessed the knight is to be being touched by Juliet. Hence, the phrase "enrich the hand" tells us that Romeo thinks she is beautiful, but it also tells us that Romeo thinks of love in purely physical terms. For Romeo, love is physical beauty and the emotions that physical touch elicits.
This passage can also be seen as being used by Shakespeare as characterization because it tells us that Romeo is no different from any other man, but it also helps to begin to point out just exactly how young Romeo is. All men put a great deal of value on physical appearance, however, younger men have an even greater tendency to do so. The fact that Romeo equates love with the physical touch of Juliet's hand shows us how inexperienced Romeo is with both physical touch and love. Had he been older and more experienced, he may have commented on her looks without focusing on the fact that she is touching the knight.
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