The metering will definitely change with different apertures. The last I shot with my 18-200mm, I had to constantly change shutter speed when I am using the 5.6 mm end of the 200mm for the same scene.
to T/S are you using spot metering ?
The thing about fixed aperture zooms do not work exactly like calculated ( e.g you cannot calculate the so called aperture of both ends of say a 70-200mm/2.8 with your N = f/D ). To simplify, if I am not mistaken the 70-200mm/2.8 uses a sort of "magnifier" within its construct to recreate the telephoto 200mm end, while able to maintain a big aperture to work.