All dealers have the capability to weigh the tongue....they may say they don't, but they actually do. However, weighing the tongue with the trailer empty will only give you, at best, an estimate at what it will weigh once loaded. That's why Skip (see above post) recommends using the trailer's GVWR as a base line. Again, 7500 lbs won't be out of line and 15% is 1125 lbs. At a 1500 payload capacity, that only leaves 375 lbs. Ask your Dad a question: would he rather push a wheel barrow loaded to 15/16th capacity or 5/8 capacity? May not be a very good analogy, but it gives you an idea of what the truck will be up against.
The 5.7 will have no problem pulling this amount of weight, but the truck itself may be at, or maybe even over, its limits. Wheel bearing, transmission, rear end gears....all will have a shorter life span.
good luck
Ron