Yes, like most here I agree that you should get the rig weighed immediately. That trailer should have at least 1,000# of tongue weight even if it is lightly loaded to get to 13%. Less that 13% tongue weight in a trailer that large is a guaranteed recipe for excessive sway and most likely the source of your problem.
The other potential problem is that you are out of or about to, run out of payload. Dodge trucks are notorious for being very light on payload. You will, when properly loaded, have well over 1,000# of TW perhaps as much as 1200# (remember the WDH adds another 100#). Most trailers the size of yours get loaded to at least 1,000#. The other indication of an overloaded truck is the fact that you have air bags AND sag. Those air bags do not change your truck numbers one ounce. When loaded with a properly set up WDH the trailer should be level to perhaps one degree of down bubble at the hitch and the truck should be level with the WDH transferring enough weight to the front axel of the truck to level it. Lubrication should not be an issue here.
Get the rig to the scales (loaded for a normal trip), and weigh it more than once and all will be made known to you. Sounds like you lack the requisite TW and or enough truck to handle it. Good luck! :C
