The simplest explanation is to think of the centerline of the trailer axles as a pivot. You will remove weight according to the ratio of the distance from the weight to the axle centerline and distance from the axle centerline to the hitch.
For example, if you put weight 10 ft. behind the axles and have 20 ft. from the axles to the hitch, 1/2 of the weight you put at the rear will be lifted from the front. 800 lbs at the rear should remove 400 lbs. from the hitch weight.
If you have a 1:3 ratio (10 ft. behind, 30 ft. to the hitch) you'll remove 1/3 of the weight (266 lbs) from the hitch, etc.
I think, but I'm not sure, that the weight you add to the back, plus the weight you remove from the hitch will be added to the axles. In the first example you'll add 1200 lbs to the axle weight (800 lbs + 400 lbs). The second example will add 1066 lbs to the axle weight (800 lbs + 266 lbs). Perhaps someone with more of a physics background can verify this?
Same thing holds for weight forward of the axles - the ratio of the distance from the axle centerline to the weight vs. the distance from the axles to the hitch determines the percentage of weight that is transferred to each.
800 lbs 10 ft. forward of the axles, with 30 ft from axles to hitch will transfer 1/3 of the weight forward - 266 lbs. The remainder will be carried by the axles.