Noah Millman sets me right on the Swan of Avon, not for the first time:

John—Just finally got around to reading your column on humanitarians, and I’ve got a nit to pick. Hamlet’s “Hecuba” line means the opposite of what you imply.
You imply that he’s saying: why do they expect me to weep for Hecuba; I
don’t even know the girl.
First of all, the line is not “what’s Hecuba to me or me to Hecuba” but
“what’s Hecuba to him or he to Hecuba.” Hamlet is not asking why people
expect him to weep for Hecuba; he *has* just been weeping for Hecuba. He’s
praising the talents of the Player King who gets him to weep for Hecuba –
who doesn’t even exist – while he can’t get himself stirred up sufficiently
by the crimes that have gone on in his own father’s house.
Here’s the speech:
“O, what a rogue and peasant slave am I!
Is it not monstrous that this player here,
But in a fiction, in a dream of passion,
Could force his soul so to his own conceit
That from her working all his visage wann’d,
Tears in his eyes, distraction in’s aspect,
A broken voice, and his whole function suiting
With forms to his conceit? and all for nothing!
For Hecuba!
What’s Hecuba to him, or he to Hecuba,
That he should weep for her? What would he do,
Had he the motive and the cue for passion
That I have? He would drown the stage with tears
And cleave the general ear with horrid speech,
Make mad the guilty and appal the free,
Confound the ignorant, and amaze indeed
The very faculties of eyes and ears. Yet I,
A dull and muddy-mettled rascal, peak,
Like John-a-dreams, unpregnant of my cause,
And can say nothing; no, not for a king,
Upon whose property and most dear life
A damn’d defeat was made”
So: Hamlet is not saying, “why should I weep for Hecuba” but “why can’t I
even make myself weep and rage for my *own* cause, when this *actor* can
weep – and make me weep – for someone who doesn’t even exist!”

I gotta stop relying on my crumbling memory resources.