Danny, there are several things that could be making your trailer sway like that.
1. Too lite of a tongue weight.
2. Improper weight distributing.
Both of these faults can be diagnosed at a CAT scale, or a local quarry, landfill, or grain scale.....those single platform scales will be a little more difficult, but can be just as accurate.
For the CAT scale weigh-in, weigh your truck without the trailer, then with the trailer without the spring bars in place, and then again with the spring bars in place. The 2 truck axles weighed during the trip across the scales with the trailer but without the spring bars in place minus your truck alone will give you your tongue weight. Your truck axles with the trailer and spring bars attached can be compared to the trip across the scales with the truck alone.......the weight of the truck front axle should be close in each of those weigh-ins.
Here is a good guide on how to use a CAT scale: http://catscale.com/how-to-weigh
Keep people and load at the same place every time across the scales.
The total weight of the combo minus the weight of the truck alone will give you the total trailer weight. The previously figured tongue weight should be in the 12-15% range of the total trailer weight. If it is less than 12%, then you will need to start loading the trailer with the heavy stuff towards the front.
3. The spring bars may not be "notched" correctly on the cam.
This is very important. The cam needs to in the exact center of the spring bar notch when going straight. You will even want to mark your spring bars on which side they are set up on, as any difference in length between the bars could cause a problem.
Also, make sure you have at least 5 links of chain between the cams and snap up brackets.