My truck also came with 20" P rated tires (Pirelli) from the manufacturer. They were of course fine as to weight rating. But when loaded up, they did squirm.
As I'm picky about handling, I looked for 20" LT's and found some slightly larger than stock, but they were very expensive and heavy. Seems the 17" LT's are cheaper than 20's for some reason. Ended up selling the 20" wheels+tires, buying 17" take-offs and mounting Michelin LTX MS/2's, LT-metric.
My overall wheel weight is about the same with the lighter rims, and I was able to sell the 20" rims at a premium so there wasn't that much of a $$ hit. And the ride is much crisper now.