Agree. 98% of wagging (low amplitude sway) can be corrected by getting a level hitch height and sufficient tongue weight (10-15% of gross trailer weight, with around 12% being a good target).
The fresh water tank is behind the axle
, and some people carry stuff on the rear receiver. Both tend to reduce tongue weight and must be compensated with weight forward.
The other 2% could be your driving style. Keep your eyes far ahead and avoid constant small steering corrections. Keep it smooth and steady.