"Romeo and Juliet" is full of light/dark imagery, which often contrasts the sun and the moon, day and night, or the idea of light as representing all things beautiful and wonderful, and darkness, contrastingly, as representing the absence of those things. However, I do think the word "light" in the two passages you refer to above has another meaning - which is quite separate from that.
"Light" to the Elizabethans could also be a pejorative word meaning "easily seduced", "sluttish" or "whorish". A girl who has sex on her first date might be referred to as "light". And this is what Juliet is worried about.
She's worried, basically that Romeo will think that she is "light" because she has yielded so quickly to his advances:
In truth, fair Montague, I am too fond,
And therefore thou mayst think my 'havior light:
But trust me, gentleman, I'll prove more true
Than those that have more cunning to be strange.
I should have been more strange, I must confess,
But that thou overheard'st, ere I was ware,
My true love's passion: therefore pardon me,
And not impute this yielding to light love,
Which the dark night hath so discovered.
She would, she says, have held Romeo off for longer - only he overheard her before she realised. So he mustn't think that she's easily seduced, because she really does mean it - and she means to prove true.
"Light" then is a kind of "false" - easy, whorish. Hope it helps!
Juliet compares their new-found love to lightening (II.ii.120), primarily to stress the speed at which their romance is moving, but also to suggest that, as the lightening is a glorious break in the blackness of the night sky, so too is their love a flash of wondrous luminance in an otherwise dark world -- a world where her every action is controlled by those around her. When the Nurse does not arrive fast enough with news about Romeo, Juliet laments that love's heralds should be thoughts "Which ten times faster glides than the sun's beams/Driving back shadows over lowering hills" (II.v.4-5). Here, the heralds of love that will bring comforting news about her darling are compared to the magical and reassuring rays of sun that drive away unwanted shadows. Juliet also equates Romeo and the bond that they share with radiant light. In a common play on words, she begs Romeo to "not impute this yielding to light love/Which the dark night hath so discovered" (II.ii.105-6), again comparing their mutual feelings of love to bright and comforting light .