Usually, when people cry, they cry out loud. But of course you can cry silently, can’t you? That hasn’t always been the case though.
To cry comes from the Old French crier (to beg, to implore), derived from the Latin quiritare (to wail, to shriek). You can see how crying was related to those concepts. There’s a good chance that if you’re wailing or imploring, you’re also shedding some tears.
Gradually though, the meaning of to cry began to drift away slightly from these early uses, and came to solely mean to weep. We can still find examples of the word used in English more in line with its original meanings though. Think of a war cry, or battle cry. There might be a public outcry about a scandal. You might hear a voice crying out for help in the middle of the night. A literal cry for help, not a metaphorical cry for help, which is of course also possible. Like crying wolf. Which I suppose you could also do literally, but it’s rare that you’d ever need to. Hopefully.
And so on. It’s clear here that to cry is being used to mean to shout or to scream, quite different from weeping, but it’s still easy to see how this meaning is derived from the original meanings. And the fact that crier means to shout in modern French has certainly helped keep this meaning in English over the centuries.
Interestingly enough, many other languages don’t associate weeping with shouting or screaming at all. Most Romance languages use verbs associated with beating one’s breast to refer to weeping, such as the French pleurer, Spanish llorar, and Italian piangere. Maybe this is down to cultural differences, which may in turn be based on linguistic differences. Maybe there’s something about English which makes it easier for us to shout and scream when we’re upset, rather than beat our breasts. Who knows, but it’s an interesting thought.