How many miles are on your RV?
Yes checking the weight will help a LOT. If the front axle is overweight, it will be compressed to far, and the tires bow outward. If to light, it will bow inward, and also not provide enough traction while turning.
I guess you already had the front end inspected, and they did not find a loose steering arm, or anything that is bent? Loose bushings can also provide bad steering. These are things to check out before installing a steering damper, or something that might hide a problem with the steering.
Of course Winnebago was much better than most RV manufactures at having the weight equal on right and left side, but still it is worth checking out.
Fred.