My understanding of the important things regarding your situation.
It tows fine with the buggy loaded and the front of truck is at the same height with the trailer hooked up and not hooked up. Take the buggy out you have problems and the tuck 1 1/2" higher.
When the buggy is out your tounge weight goes up. Adding tongue weight usually reduces trailer sway not increases it. I dont think you are experiencing trailer sway but lack of steering control because of your statement that the front of the truck is higher than unloaded. To fix this you need to distribute more weight with the spring bars. Might even need higher rated bars when empty.