If moving cargo is not a practical option, you could try a more drastic measure such as relocating the trailer's spare tire from the rear bumper to a location near, or under, the hitch A-frame. That step alone is good for 50 pounds or more swapped from back to front. If the weight and tongue check out, look over your tow vehicle and trailer to make sure they're in good mechanical condition. This is something you should do as a matter of routine maintenance anyway. Lack of alignment can make the rest of your efforts and improving stability fruitless, and will also manifest itself as unusual or rapid tire wear.
Hitch adjustment is another very important point.
First, the equalizing hitch spring bars should be adjusted such that the front and back of the tow vehicle drop equal amounts when the trailer is hitched and ready to go. For example, if the back of the tow rig drops 4 inches when the trailer tongue dead weight is resting on the ball, without the spring bars, then the front and back of the rig should drop 2 inches each with the spring bars installed and tensioned. Trailer leveling is a detail that many people overlook. Seen from the side, the trailer body should be level or dropped down slightly at the hitch ball, relative to the ground, when ready to tow. If the trailer tongue is somewhat high, with the hitch end of the frame elevated more than the aft end, in effect it changes the caster and alignment of the axle, and can lead to really squirrely towing.