I have a 12' trailer with 3" channel (don't remember the weight, but it's the lightest weight) for the frame and a 4" channel wrap-around tongue. I had to add a piece of 1.5" angle to the bottom to keep it from flexing too much, but it seems to do okay now. I use it to haul cars up to about 3k#. If the bed came as far forward as most trailers, it would be a 14' trailer, but I left the bed back just far enough that a car with its tires against the front rail is about 3.5 feet from the tailgate.
Based on my experience, a 4" channel would probably be fine. Consider that it's not uncommon for a 7k# trailer use 5" channel.