It is the simplest of sentiments and elegant in its essentialness. Hamlet says it twice, more or less, and both times as a kind of acceptance of what’s to come – the first time as the possibility of his death and the second as the inevitability of his death.
Philosophers who love this play tend to be very interested in this stance in the face of mortality. I don’t want to take that away from them. I, too, am moved by the peace that “let be” and “let it be” can bring.
If this sentence ended with a dash instead of a period, Hamlet could be about to declare something before death interrupts him again. It would be a very dramatic choice, which is sometimes better than watching someone accept death. It might be more interesting to watch him fight it.
He could be about to say, “But, let it be proclaimed throughout the land that all pirates are protected by the state of Denmark. Or let it be known that King Claudius poisoned King Hamlet in his garden and I am revenged.” But before he finishes, he feels death’s cold hand on his spine and is thus inspired to declare his death to Horatio again.
It’s the more active choice if somewhat less poetic.