What kind of problem will I have if I choose to tow 1000 lb more than the listed towing capacity.
Is that a loaded question?

Obviously, the only sensible thing for anyone to tell you is
DON'T DO IT! But that's not to say that many of us haven't done it or that it's anything unusual. So . . . ., just a few points for you to consider:
1) When a truck manufacturer establishes their tow rating they don't know whether you live in Louisiana and will be towing only at 30 mph on flat level ground, or whether you live in Colorado and will be towing over the Rocky Mountains at 70 mph, or something in between.
2)tthe tow rating is based not only on what you can pull, but also what you can
stop. The truck manufacturer doesn't know whether your trailer has brakes or not.
3) Excessive loads can cause an engine and transmission (or even the differential) to overheat, but again, the truck manufacturer doesn't know whether you're going to be towing in Texas in the summer or Alaska in the winter.
4) Some, but not all, states may stop you and might issue a citation if you're overweight, but it's been my experience that they almost never stop a personal vehicle; only commercial vehicles.
5) In the event you are involved in an accident, especially one that is your fault, your liability may be increased if you're found to be overweight.
6) Since the truck manufacturer didn't know all the things previously mentioned about your trailer and towing, you can bet they built it at least a little "cushion".
7) The truck manufacturer also didn't know how much or what kind of experience and/or training the driver will have had prior to pulling a heavy trailer.
If you don't overheat the engine or transmission, you won't hurt the truck by pulling more than it's rated for, but there may or may not be other reasons for staying within the rated limits.