This is what light meters do!!! What do you want it to do? Suggest the same exposure no matter what you point it at?
It is very easy for there to be a scene in which there are over ten "stops" difference between the darkest area and the lightest area, so if you are just getting three stops each way from middle grey, your negs are going to be quite easy to print, if not a bit flat.
This is one reason that we have grey cards. They are the best way to make an in-camera reflected meter actually give you consistently decent exposures. Read a grey card that is placed in the light for which you want to expose, and open up half a stop from your meter's recommended exposure. In-camera meters were originally designed as tools of compromise, and so they still are today. They were not ever intended to replace more accurate types of metering, but only to increase convenience. They will very rarely give you the ideal exposure if read directly off of the composition. Use a grey card whenever possible, and your exposures will improve about 90%.