Try this, Reed
You have to take into consideration where the hitch is, not just the axles in relation to the bed. You say the axles are 2/3 way back, so I will use 13 feet from front of the load bed. Now add the hitch length. I am gonna assume this length is 7 feet. Your load and trailer is supported by two things = your hitch, and the axles. Total distance between hitch and axles in this example is 20 feet. Find the middle of your load, 16k. You said it is centered on the trailer, so the center of the load is 3 feet ahead of the center of the axles, and 17 feet from the hitch. We're gonna ignore the weight of the empty trailer here, have to add it to be closer to actual weights. 17 20ths of the weight is on the trailer, 3 20ths on the truck. 16000 * 17/20 = 13600 lbs carried on trailer axles, and 16000 * 3/20 = 2400 lbs carried as hitch weight. Now add the unloaded trailer weight to get actual weights. Your original answer of 5300 lbs would be correct if your hitch was at the exact front of the load bed. Simply measure hitch to center of axles, determine load center, and figure the ratio. Clear as mud?
HTH
Jonesey