Weight distributing hitch (WDH) confused me for a long time. I think e-trailer.com had the best explanations along with some trailer forums.
Suppose your 10,000 GVWR trailer is loaded to a GVW of 10,000. Trailer tongue weight is typically 10-15% of the trailer weight if distributed evenly. That would mean a possible tongue weight of 1,000 to 1,500 Lbs. Most class IV pickup hitches are rated at 5-600 Lbs straight or 1,000 Lbs with a WDH. With this load, you can see what your pickup's hitch is asked to bear.
As I envision a working WDH, it acts much like an inverted strung long bow - pushing both ends of the bow away from the string. A WDH uses spring bars with specific weight ratings, typically 400, 600, 800, 1,000 and 1,200 Lbs. The weight rating is the maximum
up-push they provide. Pick the set that you need. They act as the bow. The trailer tongue to trailer's axles and the pickup behind the rear axle is the bow string.
Once the WDH is set up, the weight load that is in the zone of the "bow string" is distributed between the trailer axles and the pickups front & rear axles. The goal is to more
evenly load both truck axles rather than having the rear axle overloaded (sagged springs) and the front axle lifted (to where the headlights are pointing to the raccoons in the trees

). The trick is to distribute the weight to every axle so as to load each as evenly as possible and the rig will ride level.
I'll work an example as I understand it. Nothing exact here. In this example assume the weight behind the truck's rear axle is 500 lbs and the trailer's tongue weighs 1,100 lbs. for a total 1,600 Lbs. If we use 1,000 Lb spring bars and have the DWH head set up correctly, 1,000 Lbs of that 1,600 Lb load is moved between all 4 axles of the rig. The weight on the pickups class IV hitch is within design specification - closer to an actual weight of 600 Lbs. Some of the trailer"s 1,000 Lb tongue is shifted onto the two trailer axles. The 500 Lbs behind the pickup's rear axle and the ~600 Lbs tongue weight on the class IV hitch is evenly carried between the pickup's two axles. The goal is to have each axle of the truck evenly loaded and the same for the trailer.