In both cases, tears flow from the eyes. “Weep” is mostly used in writing, and is considered a literary word. When you say that someone is weeping, you are focussing on the tears, and not on the sounds that accompany it. Weeping is usually done silently, which is why you never talk about a baby weeping. Babies cry — a lot of noise accompanies the tears that flow from their eyes. One can weep for various reasons; we can weep with sorrow, and we can weep with joy. Sobbing is always done loudly; it is accompanied by a lot of noise. The heroines in our films sob a lot. Sobbing involves gasping for breath and this results in a lot of chest heaving. The word is usually associated with misery; unlike “weep”, one cannot “sob” with joy.