I'm not an expert on the WDH bit if the scale reads 600# then your hitch weight is 600#. WDH will not someone from being overweight, it helps ensure you can control the vehicle.
Since your steer 2,560# just the truck and 2,460# with your WDH, your still 100# lighter on your steers. Check your heights but you might try another link if your front still is higher than normal. Should be within 1/2" according to video from Curt Hitches.
When you hitch the trailer to your truck the rear axle acts like a pivot (think see-saw) and lifts the front end some. This reduces the weight on the front/steer tires and effects your steering. The WDH acts to lift the rear truck axle putting weight back onto the steer tires so you can properly control the truck. The WDH when properly adjust should return the front/rear bumper heights to their original unloaded ride heights (+/- 1/2"). In adjusting the ride height, the weight should return to the original ratios and protect your ability to steer.
If you change the weight on the hitch IE add battery or move gas bottle you may have to adjust the WDH but that amount of weight may not actually be enough to warrant taking up another link. I'd think it depends if it affects your ride heights. It will affect your tongue weight and your scale will tell you that. Good tool that scale.
Ever ride in a golf cart when heavy people are siting in the back and someone light is driving? The front end tends to lift/drift around making it hard to steer. It's the same principle with a TT. A 5th wheel or gooseneck trailer gets around this by putting the hitch about 1" forward of the rear axle. This places 99% of the weight over the weight on the rear axle and the 1% which goes forward to the steers which mean when you accelerate the steer tire stay on the road so you can control/steer your truck.
This is a pretty good video and may help.
How To Set up A Weight Distribution Hitch - CURTmfg.com
https://www.youtube.com/watch?v=mkewkvU8Ot8