I may appear to be a bit arrogant, but my post is from seat of the pants experience, not text book. A soft sidewall tire will produce more sway. You need no degree in engineering to determine the load capacity of a tire, it is stated on the side of the tire.
You can read many things into the load capacity of given truck, but use care and get off the couch if you want to be taken seriously. Does the wheel covers really matter? Are you making statements to impress others with what you understand from what you have read?
