i have a 2007 silverado 1500 z71 new body syle extended cab with a 2" leveling kit. im looking to increase tire size and im looking to see if this size jump would work

im currently running some 265 70 r17 i like my stock wheels but i am interested in purchasing some Nitto Trail Grapplers size LT285/70R17 E121/118Q these tires are about an inch and 3/4 taller than my old ones and im wondering will i get any rubbing?should i stick to the same size and just go that route. i would like some taller/wider tires but i dont want to get my MPG destroyed as well any help would be greatly appreciated thanks!