Is it the entire rack flexing, or just play in the receiver socket? Most racks have play in a standard 2" socket, and it results in a little sway and/or bounce as a result. One of these anti-rattle clamps can reduce or virtually eliminate it:
I used one of the 2-bolt models on an old rear-hitch motorcycle carrier with a 500lb motorcycle on a few occasions, and it was great at minimizing the sway and bounce, and unifying the rack with my truck.
There is a bit of movement but not much. A hitch stabilizer helps and I run tow straps up to the roof rack to take a little play out and add some piece of mind ala @Alaskan 's solution from a while back
There is some flex. I take it easy going over speed bump or rail road tracks. Make sure the rack is very tight in the hitch by turning the tighting knob as far as possible.
I use a KAC (Kick Ass Carriers) platform rack on my pickup or Rialta RV. They come with a special bolt for locking to the receiver, and the bolt has its own lock to prevent its removal. I have had very little sway or wiggle, even on rough roads. That's with a 65+ lb. ebike and a Townie regular bike.
There is an anti-wiggle device in the tongue of the Thule Easy Fold Hitch rack. As one tightens the knob, a wedge slides inside the receiver, tightening up the connection. To get it right I find it necessary to move the rack back and forth & up and down while tightening the knob ever further till I get no more turns on it. At that point there is far less movement. Adding the two Curt straps from the roof racks to the clamp mount on the easy fold helps with both weight support and any remaining wiggle.
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