Not sure about Chevrolet, but GMC has a Towing Guide which includes the Acadia (Traverse's twin). There it says that a WDH is "not required". Also that tongue weight should be max 600# (or less so as not to exceed the SUV's GVWR or rear GAWR).
500-600# limit for a class III weight-carrying hitch is pretty typical. Ford tells me I can only carry 500# on my truck's hitch.
I would load up your SUV and trailer and try towing it to the nearest scale to check the GVWR and GAWR.