In part six, Jotaro loses both his memory and stand disc, this causes him to lose consciousness and his body starts to decompose. After gaining his stand disc he comes back to life, but loses all his memories and his will to live. This causes the muscles to decompose which would eventually cause Jotaro his life if it weren't for the return of his memory disc. Weather lost his memories but this didn't happen to him, why?
It is because when Pucci claimed Jotaro's disc, he already had a stand, and by taking his stand along with his memories, there is no way for him to recover said memories, as his stand is also taken away from him, this is also linked with the fact stands are basically the representation on a person's soul, getting your stand revoked is essentially as if somebody tore your soul away from your body, leaving you a husk. That did not happen to Weather Report, because his stand was not yet awakened, and if you do not have a stand at the time where your disc gets stolen, there is only a memory disc, however your potential to acquire a stand is still there, meaning your soul has still not yet given up, which was the case with Weather, after his memories disc gets stolen, he awakens his own stand, making him capable to live even without his memories.