I think your gas mileage might decrease a tiny bit , body roll might increase but you would have more grip , might be a little less nimble too if you go for the 85's -- but these are only guesses .
Honda picked that tire size for a reason - 75's
But I see your problem , better tire selection . I would check Honda Fit forums and see what performance upgrades work best for your car when you alter tire size , in your case width , they will also recommend the best tires too .
The diameter doesn't change , just the width if you go with 85's .