Franzmann, not sure if the tail is wagging the dog all the time or just when big trucks pass but it is usually caused by one of several problems.
1) hitch not set up properly
2) weight in trailer not balanced well
3) too little/much tongue weight.
4) towing with a short wheelbase SUV.
1,2&3 are fixable with a little time and knowledge, 4 is more costly (ie buy a truck)
You should be able to tow that size comfortably with a proper setup as long as the weights are ok. First you need to load the trailer and T4R as you would to camp. Next, hook it up as per the hitch manual. Some rear sag is normal (1-2" without the airbags) and the front should return to close to the unhitched height. Airbags can sometimes mask the problem as well since it looks level hitched up, but they dont do anything to transfer weight to front, so WD bars usually aren't tensioned enough. Turn the system off when setting hitch up. Then take it to the nearest scale and get it weighed. Weigh the T4R alone, front and rear axle, hook up and do the same as well as the whole combo. This will tell you how much the trailer weighs and if enough weight is being distributed. Also, unhitch and weigh the tongue (google the bathroom scale method). The tongue should be around 13% of trailer weight and hopefully not above reciever max. You may be able to move your gear around to help get the numbers close or adjust the WD bar tension (may need a better reciever to do it).
Lastly is the hitch. Friction sway control is the weakest type. In order for it to function it must be cranked down completely. If the above suggestions prove ok and you still have problems with sway then I would suggest a different style of hitch with built in sway control such as an Equil-i-zer or Reese dual cam. If you have the means, a Hensley Arrow. I towed a 26'BH (5500lbs) with my '04 V8 with this setup. In any case you will get blown by the big rigs, can't stop it completely but you can minimize the effects. Lifts or oversized A/T tires will exagerate the effect. You may need to upgrade the stock passenger tires (soft sidewalls) to load range D or E for better stability and make sure they are aired up accordingly.
Good luck.