Juliet’s interruption can be played to either comic or serious effect. She wants Romeo to be “constant,” but ironically keeps changing her mind about what he should swear by. Yet she’s genuinely worried that he won’t be able to live up to any grand promises: “if thou swear'st, / Thou may prove false.” This element can be emphasized if the actor playing Romeo sounds self-serious or over-the-top when she cuts him off.

https://youtu.be/FHoaPLO6Zd8?t=6m34s

prove false: (1) prove to be lying (when you say you love me); (2) end up being sexually unfaithful.

Romeo has been talking about nothing but love (he’s used the word nine times in the scene so far), so Juliet’s concern is not that he express the emotion, but that he back it up with a firm promise.

So forgive me, and please don’t take my yielding to love so quickly—which you’ve only found out by overhearing me at night—as a sign that I give my love away lightly.

Juliet is wary of being thought “easy,” naive, or both.

discovered: uncovered.

I wouldn’t have them see you here for all the world.

See above. Juliet is consistently the more realistic of the two. She has no illusions that love is protection against death.

Too much pride is better than too little; better to overestimate your worth than sell it short (and neglect your own interests as a result).

In Grace Paley’s story “Goodbye and Good Luck” (from The Little Disturbances of Man, 1956), the actor Vlashkin quotes this line as a grand excuse for his egotism:

…there is a line in Shakespeare in one of the great plays from the history of England. It says, ‘Self-loving is not so vile a sin, my liege, as self-neglecting.’ This idea also appears in modern times in the moralistic followers of Freud…

If she weren’t hidden by darkness, Romeo would see her blushing for what he’s overheard her confessing. (LUV!)

The issue of women “painting” their faces with makeup was a controversial one in Shakespeare’s era (as it is in many religiously conservative societies). See Hamlet’s condemnation of women in his “Get thee to a nunnery” speech:

I have heard of your paintings too, well enough; God has given you one face, and you make yourselves another…

Juliet’s image may contain an implied contrast with cosmetics, suggesting that her cheeks would be painted only with the blush of “maiden” innocence.

Romeo’s image of tearing up his own name eerily reminds us that he is a literary character whom the playwright has “written” into existence–and can destroy, too.

Via the Craven Museum & Gallery