I've shot quite a bit without changing my exposure settings at all. For street photography with TriX or HP5, I normally focus at 10ft/3m, set the shutter to 1/125, and the aperture to f/8 or f/5.6. If it's a particularly dark day, I'll keep the settings and push the film. It's not perfect, but it doesn't have to be, and sometimes it's the difference between getting the shot and not.
One thing to consider re: Weegee is that he was shooting with a flash, which would have made results from relatively fixed settings far more consistent.