I have an 03 4x4 Tahoe and the same question. From what I understand, you can go with 265/75 or 285/75 on the stock 16" rim. Try a search on the Silverado forum, a lot of people run 285/75s on their Z71s.
I've heard where the 285/75s will rub when the steering is hard over but then some say they don't have that issue. Likely it depends on which tire you choose.
The 265/75s don't seem to be an issue and I think they were an option on the Tahoe/Yukon lineup...probably your best bet.
Below are links to some pictures of Tahoes with the 285/75/R16s. I couldn't find any with 265/75s but maybe someone here can add some.
http://www.cardomain.com/ride/770448/1
http://www.cardomain.com/ride/654776