Should I install a WDH?

The way I see it is thus:

1. You can use a WDH with that combination and have a somewhat reasonable setup.

2. You can go without the WDH until that combination takes you to the scene of the accident.

whoops, mistake there, 

Gross Combined Wt Rating (lbs) 13,250

Empty weight is irrelevant.  Gvwr is 7700, so figure 900-1000 hitch weight.  Is the max tounge with or without wdh?  Usually it's higher with wdh. At  best you will be pushing the limit if not exceeding it. 

Also what does the payload sticker on the door say?  Good chance you are over payload. Hitch weight counts against payload. Add in people and gear and you are likely north of 1500-1800lb. 

If you can keep within the ratings,  a wdh is a good idea. 

simple answer is yes.  the weight its self is only part of it.  the extra tie in between the truck and the trailer makes the ride so much better. 

your not realy putting 90lbs on the hitch, well you are but you are using the system to transfer a portion of that weight to the front tires so the truck is more evenly loaded.  

Personally I wouldn't like the idea that the hitch ball is not replaceable. Stuff happens and I consider the ball as a wear item. I would return that hitch if you can and order an Equal-i-zer hitch. which is 0nly $845 for a 1000, 10,000 lb hitch.

Yes, you need a WD hitch and almost as important, one that has built in sway control.  I tow with a half ton TV and my trailer weighs in at just about 6500 lbs when we are out on the road.  I have measured this a few times over the years as Washington State leaves their weigh stations open and functioning even when the sign says "closed"  I can pull in, position the trailer on the scales and look in the side door to see the measurement. 

I don't know anything about this hitch but it looks much like my Equalizer in design only with the scale on the ball.  Setting up mine took a few adjustments but it rides level, is not hard to hook up and provides a solid connection between truck and trailer.  I recommend a WD hitch, especially when you have a half ton.