Another quick reference: I have a 2001 Silverado that is much like yours = 2WD, extended cab, 6' bed. Undersides shouldn't be too much different.

I have 265-70-17s on mine, no lift and no rub but that is with some new wheels that have a slight off-set.

I had some 265-65-16s on my stock wheels that did rub. If you are keeping your stock wheels, some 265s may be the max.