I appreciate most of you guys are American, but I can give a European point of view!
I was a trailer and towbar manufacturer for over 25 years so know a bit about the subject.
In the eu, towbars have a 'd' value and an 's' value on the spec plate. The 's' value is the maximum nose weight (or tongue weight). To exceed that would be illegal.
We do things a bit differently here.... The design nose weight of trailers is generally accepted to be between 4% and 7% of the gross weight.
There is no doubt that (within the constraints) the higher the nose-weight, the more stable the outfit should be. As you said you're guessing at 2400lbs gross, then nose weight ought to be between 96 and 170 lb.
As some have said, there are various ways to achieve this....
1. Shift the load.
2. Lift the towball.
3. Shift the axle.
4. Add/remove ballast.
How much will depend very much on the configuration of your trailer, single/tandem/tri axle, and of course, the limits of your towbar and towing vehicle.
Measuring nose weight with bathroom scales is a simple operation on single axle trailers. I would go directly on the platform of the scales (using a sheet of ply to spread the load). On double (and tri) axle trailers, it is essential for the coupling height to be the same height as when hitched on to the vehicle, for results to be meaningful.
I've posted this in the hope it may help some European cousins!