is there an area that shows watts per kg?
Not directly. A few of the athlete profiles are listed in W/Kg (Road Sprinter, Puncheur, GC Specialist & Climber). You can find these in the RANKINGS tab of the main page. Hope that helps!
If you set your profile as Climber or GC you will see Watts/Kg On your “My fitness” page
Wouldn’t it be better to to allow to switch between watts and watts per kg on the rankings chart? For me the chart is pretty useless. For durations which are shown as W/kg I’m around 50%. For those in Watts I’m around 25%.
I would also like to see number in wkg, in addition to watts. Since weight can fluctuate, I track wkg more than watts. In a diagram as below, it would be much more helpful. Especially since I am a light rider. Also, as you can select male/age, I would also like to add a weightspan. as ~61kg rider, being compared in watts is depressing 
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What is the reason some are in watts and some are in wkg in the rankings page?
What makes sense for the role. As an example watts are king fir a timetrialist whereas a climber cares more about w/kg than raw power
10 sek = watts, 2 min = wkg, 3 min = watts, 4 min = wkg,
5 & 6 min = watts, 8 & 10 min = wkg,
20 min and beyond = watts.
It feels a little random
Just set your athlete type based on whether you prefer to see the values in W/kg vs W. 
Also, without syncing of the weight from Garmin or other eco systems, the weight is probably not up-to-date in Xert.
Where do I set my athlete type?