I'm looking to buy the towing trailer ball and and towing ball mount from an oem Toyota supplier online. Which size ball do I need? They offer a 2" and 2 5/16" ball but don't specify the weight rating on them. I will be using it to tow an acura integra on a trailer from Vegas to Phoenix a couple times a year, so I will be going through mountains. The car weighs about 2700lbs. I'm guessing the bigger 2 5/16" ball can handle more weight and would be the safest option to get. I also noticed that the smaller 2" ball is more expensive, why is that?