Just because the rear axle weight "might" be approx. 3000 lbs, that doesn't mean that he has 3100 lbs of payload capacity....That's NOT how it's calculated! Bad Advice period.
Now your just runnin' your lip. Thats exactly how a trucks actual in the bed payload is calculated.
Numbers of axle splines and axle diameter has nothing to do with how much load it carries but rather how much twist it can withstand.
Axles on a full floater rear axle don't carry weight...just the housing bearings and wheels/tires. Like I mentioned get the F250 with the heavy service package /camper package and you get the suspension as the F350 SRW.
The smaller axle tube diameters/smaller springs mentioned are for the 6.2 gasser.
As kdbgoat says part numbers are all the same.... per Ford folks.
This from FTE website on answers from a Ford truck engineer Q&A.
F250 vs F350 SRW AXLES
The axles are identical as is every other part between the 250 and SRW 350. The 250 is de-rated from the factory as are it's axles. The two small differences generally sited between the two, the 4" vs. 2" block and overload spring, can actually be ordered on the 250. The 4" block comes with the FX4 and plow prep and the overload comes with the camper pkg. So, a 250 can be ordered with every part identical to the 350 SRW. Here are the part numbers for a 2012 F250 vs. F350. I chose 2012 but the results are the same if you search any year of the current generation from 11-15.
F250 Left Rear Axle BC3Z4234C
F250 Right Rear Axle BC3Z4234D
F350 Left Rear Axle BC3Z4234C
F350 Right Rear Axle BC3Z4234D
And here are the links to verify:
2012 F250 https://www.silverstatefordparts.com...R%20SUSPENSION
2012 F350 https://www.silverstatefordparts.com...R%20SUSPENSION..
Anyhow .....the OP F250 won't have any issues legally/safely towing that size trailer.