I have these on my c7 at the moment
they are Kelly 265/75R16 and the tread is pretty chunky and they didn't rub at all on the standard suspension even after I had put a steel bar on, winch with steel cable, 2nd battery in engine bay, bash plates etc.
all that made the front sink pretty bad which forced me to get new suspension but the wheels never rubbed on the vehicle.
I also have a set of coopers at3 which are 265/70/R16 and they are great for long road driving, nice and quiet and grip very well in the wet
anything bigger than 265/75 on a 16 inch rim will probably hit, you might be able to get a 15 inch rim and put a higher profile tire on but make sure the rim clears the brake calipers and discs before buying.
you might be able to fit 285/70R16 on but I would also test fit them before buying as they might hit in the front at full lock of the steering.
I wouldn't go up in rim size they don't do as well when you deflate them to drive on sand or mud(less surface area?) I see people putting 20 inch rims on and then wonder why they cant tackle the beach very well.
anyone with a Colorado 7 if they are going to add the stuff I did to mine you will need better front suspension it sinks pretty bad when you add 200 to 300 kg to the front and would only get worse over time with the constant load on it.