I know 325's rubbed like crazy on mine and it had a leveling kit. 315's will probably rub, a 295 is a safe bet. I have 275/65/20's right now with no issue. But the old tires rubbed against the leaf's and that was with a proper backspacing on the wheel without having them stick way out there.
I had 315/16's and it sucked. They were on it when I bought it. Eventually I went down to 285's. I went w/ an "E" rated tire and haven't looked back. I keep them aired up to 80psi and it has had a very positive effect on my fuel mileage. I may even go back to 265's next time around. The diff between 265 and 285 is fairly minimal, I think 4%? Someone correct me if I'm wrong. Anyhow, "E" rated tires rule. Our trucks our heavy, "E"'s are the perfect match. (IMO)
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