#1. A 5er with a 16,500# GVWR is DRW area!
#2. The 2,900# dry hitch may not change much, but will likely put you well over the GRAWR, which is likely based on tire capacity.
#3. Just for comparison, I carry an 11,000# (Loaded) 5er, with our 2001 Ram 2500 and I am right at 10,000# GVW for the TV, with 2,000# of hitch weight. I carry about 5,500# on the rear axle rated for 6,084#. So you will be over GVWR, Not so bad, but not good. Over GRAWR by likely 300#+, not good, and likely over max tire ratings Very Bad!
