I HOPE you don't have anything stuck on the trailer bumper such as bikes, racks etc...those are tail-waggers on small trailers.
I think you have two basic problems: short wheelbase vehicle AND way too light on the tongue. You can't do anything about the tug, of course, so you'll have to address the tongue weight somehow.
First thing I'd look at is coupler height- that should be dead level when hitched, or very slightly low. If it's high, you effectively lighten the tongue. Lowering it a bit below level has the opposite effect and might be worth trying if you can't beef things up by any other method.
Next, the load. It must be poorly distributed...move whatever you can ahead of or over the axles, and empty any tanks you have at the rear.
And as noted earlier, do make sure all tires are properly inflated...flab in that department certainly doesn't help!
