The trailer wont sink the boat. Teh weight rating is the max amount of weight the boat will hold and still float even when completely full of water. Lets say your boat is rated at 1,500 pounds. You could load it with 1500 pounds of gear, gas, people, motor, and equipment, pull the plug and fill the boat and it would still float. This is a safety factor so the occupants can hang onto the boat until help arrives.
Heres the video of Bill Dance and the trailer incident.
As you can see the boat didn't have any trouble with the trailer attached. Handled like a dog, but she floated just fine.
YouTube - Bill Dance Fishing Bloopers - Dance launches with trailer