How does Shakespeare contrast joy vs. sorrow in Romeo and Juliet?

Your question is quite large in potential scope, so I will
focus on the use of comic relief in the play.  Shakespeare actually used comedy quite a
bit (and quite effectively) in his tragedies.  If you think about it, there's quite a
bit of tension that develops when an audience is on pins and needles waiting to see what
will unfold as the drama builds.  Shakespeare understood this and often inserted comic
moments (even in highly dramatic scenes) to help relieve the tension for the audience. 
So, in this answer, I'll be using the terms joy and sorrow to relate to the audience's
experience of the events rather than the characters'.

Two
major characters in Romeo and Juliet that can be noted as central
to the dramatic plot, but also providers of comic relief, are the Friar and the Nurse. 
And both provide comic relief for the audience in highly sorrowful/tragic
moments.

Once the Nurse discovers Juliet's cold, seemingly
dead body and calls the Capulets in to see their daughter, Shakespeare gives her some
rather awkward lines:

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O woe!  O woeful, woeful, woeful
day.

Most lamentable day.  Most woeful
day

That ever, ever I did yet
behold.

O day, O day, O day, O hateful
day.

...O day, O day, O woeful
day.

Compared to the speeches
of Lord and Lady Capulet that speak eloquently of their love for Juliet, this text seems
to be more an echo of Bottom's silly send-up of Tragedy as Pyramus in the mechanicals
play in A Midsummer Night's
Dream.

However, what if Shakespeare was using
the Nurse to show how sometimes in the most tragic circumstances, people behave in
humorous ways?  If the actor playing the Nurse puts everything they have into these
lines, it seems that the audience will potentially find it funny.  And at that moment,
Shakespeare has shown, in his genius, the comic in the
tragic.

A smaller, but equally telling use of a comic
moment smack dab in the middle of a tragic event is at the end of the play when the 
Friar is hurrying to get to Juliet's tomb ahead of Romeo.  The Friar's
text:

Saint
Francis be my speed.  How oft tonight

Have my old feet
stumbled at graves.  Who's
there?

This text indicates
some very old and basic comic devices:  one -- that he stumbles (a character tripping
onstage is always funny) and two that he is immediately jumpy, wondering what bogey man
is there in the darkness of the tomb.  The moment is creepy and tense for the audience,
and it seems just right, dramatically, for Shakespeare to have intended this small
moment with the Friar to provide some comic relief.