In the old days you never heard of anyone concerned with weights...if your vehicle would tow it then tow it. Back then we bought a TT without any coincern to if it was too heavy for our tow vehicle (1978 Ramcharger). We towed the TT for many years without any problem.
Then it was time to get a new RV and we chose to go with a 38ft 5th wheel. At that time I had a 1984 4X4 Chevy 2500. Immediately I could tell the trailer was too much for the truck. For a couple of years I tried to live with it, but the truck began to have problems. I picked up a 1986 C3500 crewcab long bed dually. It handled the trailer well except I never felt like it had enough stopping power. The truck was rated for a 10K 5th wheel and our 5th wheel had a gross of 13K. Every downhill was white knuckle time.
14 years later I finally bought a truck that had more than enough capacity for our 5th wheel. A 2007 Chevy Kodiak C4500. This truck makes towing a dream. Plenty of power and plenty of stopping power. No more white knuckles.
The moral: you can tow a beyond capacity trailer but the stress on you and the tow vehicle isn't worth it.