Tears

Richard. I cannot weep; for all my body's moisture
Scarce serves to quench my furnace-burning heart:
Nor can my tongue unload my heart's great burthen;
For selfsame wind that I should speak withal
Is kindling coals that fires all my breast,
And burns me up with flames that tears would quench.
To weep is to make less the depth of grief:
Tears then for babes; blows and revenge for me
Richard, I bear thy name; I'll venge thy death,
Or die renowned by attempting it.
(Henry VI part 3, 2.1.706-715)

In this speech by Richard, later Richard III, or as he is described in the 1595 published version of this play, "Crookeback Richard," he, as the son of Richard Plantagenent, Duke of York, mourns his father's death and plots revenge. However, he cannot weep for his father and goes so far as to disdain tears: Tears then for babes. Richard's inability to display sorrowful emotion hints at his inhumane and ambitious personality that will display itself in violence against his own family.

In contrast, Richard's father - the Duke of York, whose single-minded ambition for a throne has driven the violence in the three plays - values revenge, but is not impervious to tears of sorrow. Upon hearing of his young son Rutland's death, he weeps before Queen Margaret and Clifford, who has killed the boy:

Richard Plantagenent (Duke of York). O tiger's heart wrapt in a woman's hide!
How couldst thou drain the life-blood of the child,
To bid the father wipe his eyes withal,
And yet be seen to bear a woman's face?
Women are soft, mild, pitiful and flexible;
Thou stern, obdurate, flinty, rough, remorseless.
Bids't thou me rage? why, now thou hast thy wish:
Wouldst have me weep? why, now thou hast thy will:
For raging wind blows up incessant showers,
And when the rage allays, the rain begins.
These tears are my sweet Rutland's obsequies:
And every drop cries vengeance for his death,
'Gainst thee, fell Clifford, and thee, false
Frenchwoman.

Earl of Northumberland. Beshrew me, but his passion moves me so
That hardly can I cheque my eyes from tears.
(1.4.577-592)

And I think that this capacity for sorrow and emotion in York is one of the reasons that I actually care about his fate. Though throughout the three plays York has shown himself to be a completely amoral opportunistic schemer obsessed with his royal ambitions, he also is very brave, loyal to the members of his faction, and - as we see here - loving to his sons, who worship him. These qualities allow us to overlook his viciousness and hope that his prayer for his soul is answered: "Open Thy gate of mercy, gracious God!" (1.4.620)