What is te Largest size tire diameter that I can put on my 2004 Sierra 2500 HD without lifting it? Do I have to change the wheels to get the best results?

The largest would be a 285/75-16 but you would need to get at least a 7.5" wide rim to run that size. The largest that will fit on the base model stock 6.5" rim is a 245/75-16.