How does Shakespeare show that Lord Capulet has changed over the course of the play?

When we first meet Lord Capulet he is discussing with Count Paris the potential marriage between his daughter Juliet and the Count. Paris is very interested in marrying Juliet. While it would be a good match because they are both from the upper class of Verona society, Capulet is hesitant because his daughter is still very young and she is his only living offspring. Capulet says in Act I, Scene 2,

My child is yet...

When we first meet Lord Capulet he is discussing with Count Paris the potential marriage between his daughter Juliet and the Count. Paris is very interested in marrying Juliet. While it would be a good match because they are both from the upper class of Verona society, Capulet is hesitant because his daughter is still very young and she is his only living offspring. Capulet says in Act I, Scene 2,

My child is yet a stranger in the world.
She hath not seen the change of fourteen years.
Let two more summers wither in their pride
Ere we may think her ripe to be a bride.

Paris reminds Capulet that even younger girls are already married and have borne children. Capulet is well aware of this and it is precisely why he thinks Juliet is not ready. Capulet has many excellent qualities in the beginning of the play. He wants what is best for his daughter.

Although Capulet is ready to fight in the opening scene during the street brawl caused by Tybalt, he is not inclined to fight at his party. When Tybalt discovers Romeo and wants to fight, Capulet urges restraint and even compliments Romeo. He says in Act I, Scene 5:

Content thee, gentle coz. Let him alone.
He bears him like a portly gentleman,
And, to say truth, Verona brags of him
To be a virtuous and well-governed youth.
I would not for the wealth of all this town
Here in my house do him disparagement.
Therefore be patient. Take no note of him.

Once again Capulet shows redeeming qualities in his patience and praise of the son of his mortal enemy.

Unfortunately, Capulet loses patience later in the play. He changes his mind about Juliet marrying and, in the wake of Tybalt's death, arranges the marriage between Juliet and Paris. He thinks it a good idea to bring a "day of joy" to make up for the loss the family feels. When Juliet is obviously against the idea he loses his temper in Act III, Scene 6:

How, how, how, how? Chopped logic? What is this?
“Proud,” and “I thank you,” and “I thank you not,”
And yet “not proud”? Mistress minion you,
Thank me no thankings, nor proud me no prouds,
But fettle your fine joints ’gainst Thursday next
To go with Paris to Saint Peter’s Church,
Or I will drag thee on a hurdle thither.
Out, you green-sickness carrion! Out, you baggage!
You tallow face!

Rather than show patience, Capulet insults his daughter. He has drastically changed his mind. A few days ago she was too young, but now she must marry Paris or face being disowned. This change in Capulet's personality may be more a vehicle of Shakespeare's plot than a true condemnation of Juliet's father. Shakespeare needed the plot twist to set up Juliet's fake death and the eventual double suicide.

Upon finding Juliet supposedly dead in Act IV, Scene 5 he expresses his profound grief:

Despised, distressèd, hated, martyred, killed!
Uncomfortable time, why cam’st thou now
To murder, murder our solemnity?
O child! O child! My soul and not my child!
Dead art thou! Alack, my child is dead,
And with my child my joys are burièd.

In the end, we have sympathy for Capulet and the role he plays in the death of his only daughter. The feud he and Montague engaged in led to final tragedy.