The Gross Axle Weight Rating for the Promaster is 4,630 pounds Front and 5,291 pounds rear. In order to support the maximum weight rating of 5,291 rear, each tire must therefore be capable of supporting 2,645 pounds. The Promasters now come with the Nexen Roadian CT8 HL, which is rated at 2,680 pounds per tire, which technically makes it sufficient.
Any tire designated for Light Truck, having the LT in its size, with a rating of at least 2,645 will work. But, if you find a tire that does not have the LT rating, and is a P metric or Euro metric size, then it has to have a higher rating to use on the van. LT rated tires are designed for vehicles with a higher center of gravity and a greater ability to carry heavy loads for longer amounts of time. When using a P metric size (225/75-16 versus LT225/75-16) then you have to calculate 91% of the load rating as the maximum. For example, if you find a P metric tire with a rating of 2,700 pounds you would think it is enough, but a P metric tire rated at 2,700 pounds for a car is only rated at 2,700 x 91% = 2,457 pounds when used on a light truck, van, or SUV.
Here's where it gets interesting and specifically applicable to the Promaster. The early Promasters came with a Euro metric 225/75-16C, rated at 3,195 pounds. When used on a light truck, van, or SUV then that tire is actually rated at a maximum load rating of 3,195 x 91% = 2,907 pounds. Still overkill, but not by as much as we originally thought.
To answer Dooman, if you need replacement tires for your Promaster, look for the LT225/75-16 versus the 225/75-16 tire size, and you will see there are plenty of options. On the TireRack.com web site, if you select a 2015 or 2016 Promaster there are 22 tires that come as possible replacements. PerformancePlusTire.com has 93 tires listed in the LT225/75-16 size.