How can we tell through the character that there is hate in Romeo and Juliet?

Even before the play begins, hateful language (in bold) is established by the Chorus in the prologue:

From ancient grudge break to new mutiny,
Where civil blood makes civil hands unclean.
From forth the fatal loins of these two foes
A pair of star-cross'd lovers take their life;
Whole misadventured piteous overthrows
Do with their death bury their parents' strife.
The fearful passage of their death-mark'd love,
And the continuance of their parents' rage,

Hate is most embodied in Tybalt, who says:

What, drawn, and talk of peace! I hate the word,
As I hate hell, all Montagues, and thee:
Have at thee, coward!

After the brawl the Prince warns both families:

Canker'd with peace, to part your canker'd hate:
If ever you disturb our streets again,
Your lives shall pay the forfeit of the peace.

Romeo soon after meditates on the absurdity of the families' hate, using oxymorons:

Here's much to do with hate, but more with love.
Why, then, O brawling love! O loving hate!

Juliet echoes this after she finds out she's fallen for a Montague:

My only love sprung from my only hate!
Too early seen unknown, and known too late!

Romeo, in the balcony scene, hates his name:

I know not how to tell thee who I am:
My name, dear saint, is hateful to myself,
Because it is an enemy to thee;
Had I it written, I would tear the word.

And he foreshadows his death, which is ironically caused by love as much as hate,

My life were better ended by their hate,
Than death prorogued, wanting of thy love.

Tybalt picks a fight with Romeo, thus causing his death...

Romeo, the hate I bear thee can afford
No better term than this,--thou art a villain.

...and Romeo's exile by the Prince:

Immediately we do exile him hence:
I have an interest in your hate's proceeding,
My blood for your rude brawls doth lie a-bleeding;

Romeo again foreshadows his suicide to the Nurse and Friar Lawrence:

As if that name,
Shot from the deadly level of a gun,
Did murder her; as that name's cursed hand
Murder'd her kinsman. O, tell me, friar, tell me,
In what vile part of this anatomy
Doth my name lodge? tell me, that I may sack
The hateful mansion.

Juliet pretends to hate Romeo, but really she hates Paris and her parents' idea of arranged marriage:

I will not marry yet; and, when I do, I swear,
It shall be Romeo, whom you know I hate,
Rather than Paris.

When Juliet pretends to die, her mother says:

Accursed, unhappy, wretched, hateful day!

Lord Capulet follows:

Despised, distressed, hated, martyr'd, kill'd!

Finally, the Prince echoes his earlier speech:

See, what a scourge is laid upon your hate,
That heaven finds means to kill your joys with love.

So, hate is the flip side of love.  It's an easy word with which to rhyme.  Montagues are hated.  The name "Montague" is hated.  Love is hated.  Death is hated.  Villains are hated.  Exile is hated.  Peace is hated.  Arranged marriage is hated.

So, what have we learned?  Don't hate the play-er, hate the game...