Going to suggest adding water to any front tanks you have to increase the tongue weight if you have room to with your GVWR. I had a similar problem (without the tire change) when I first got my trailer and it was from not enough tongue weight, loading too much heavier stuff (cases of drinks, gallons of bottled water/etc) too far aft of the trailer axles. Realized that between the rear loading of the trailer and driving without water in the fresh water tank (at the front of the trailer), I had significantly changed the balance of the trailers weight over it's axles, inducing a sway problem I had never had in the 3-4 previous trips.
Now that I know to put my heavier stuff as far forward as I can in the trailer, I can travel with or without water in the tanks and not have issues but was one of those things I had to learn about as a new RVer.