Sway Bars

Set your bars on a flat surface. Does one of them look bent or are they both the same?
Look at the hitch head. What is its condition? Is there any sign of looseness in the hitch head when you put the bars in? Do the bars look like they are at the same angle when inserted into the head (before putting the bars into the L brackets)? Is there any obvious damage to the hitch head or the shank (twisted, for example?
Look at the hitch receiver without the hitch head installed. Does it look square with the vehicle? When you look underneath where it is attached to the frame, does it look like there is any damage or twisting?

If you do all of this and still can't see what could be causing it, it might be time to take a trip to a place that can help you diagnose this. If it isn't working right, you could be putting yourself and others at risk.

Check your tire pressures.

We tow our 172 using a Fastway E2 and it works very well both on windy mountain passes and the freeway.  The ride is stable and it's comfortable to drive with our Dakota.  The truck is a little on the high side so initially the trailer was a little too high at the hitch end.  I put in the lift kit from Forrest River and now it rides quite level and fits the hitch just fine.  It's easy to hook and unhook.  I use the tongue jack to position the height so the bars slip in and out without any tension.  The hitch comes with a pry bar to take off the tension bars, but if they're under a load you could easily lose a finger if you put one in harms way.  

We have used a basic sway bar on both our '08 and '13 Explorers.  No issues with either even when crossing the Midwest into the Rockies where we have experienced 25 + mph cross-winds.

I took Charlie's advise as well as others on this board and bought the Fastway E2 6000/600 and have been very happy with the choice.