I hate to jump in on Roger's area of expertise, but the reason it was done this way is that a 4 axled plus pilot and trailing truck locomotive (2-8-2) has a long rigid wheelbase which was far to long to negotiate the Uintah's extreme curvature. Some locomotives such as the 2-8-0's on the C&S and I believe the EBT's 2-8-2's have blind drivers ie. the two center driving axles have no flanges. This allows them to take tighter curves without spreading the rail or derailing. Also more lateral play can be added to the center axles so they can float to one side in a curve. This also means the pins and bushings have to be looser on the side rods to avoid binding, which leads to pounding and possible bearing failure, loosening of the pins in the drivers or possible other catastophic failure, so there are practical limits to the amount of lateral motion. The pilot and trailing truck can move from side to side and do so in a curve, but they usually have centering devices that help guide the locomotive into a curve, so at least in the type of pilot truck centering device I am familiar with, side motion of the truck tends to lift the spring rigging to the truck causing more down pressure on the truck, or rather an increased weight distribution on the truck. So while this helps keep the pilot truck down against the rail in a curve versus climbing the rail and derailing the whole thing, it isn't really free to swing to an extreme in a tight curve. This also limits a locomotives ability to take a very tight curve sucessfully. I think some engine have a trailing truck built the same way, and others (like 19 and 20) simply have springs the trailing truck shoves against as it moves sideways in a curve. I think this is mainly to keep the truck from hunting from side to side on straight track.
Now all of this said as to the why's and hows of bending a locomotive around a curve, the Uintah had some extremely tight curves. I think originally 66 deg. at Moro Castle. A two axled truck off of a tender, pass. or frt. car has a short rigid wheelbase. The independent trucks on a Shay, Heisler or Climax likewise are a short rigid wheelbase built with a sinlge pivot point in the center of the bolster like a freight or pass. car. Tender trucks usually are heavier in construction than regular freight trucks and have a larger jounal and bearing diameter, and therefor would be more suited to temporarily supporting the weight of the #30. Presumable to do so and keep the arangement such that the trucks could pivot in the curves, some sort of temporary bolsters had to be constructed under each end of the locomotive.
The Uintah/SVRy 2-6-6-2's while a much larger/longer engine that a 2-8-2 would actually be far more flexible because the rigid wheel base would only have 3 driving axles then articulation then 3 driving axles, with the pilot and trailing truck a mentioned earlier. I think even so, I read somewhere that the 66 degree curve was opened up a little bit to allow these engines to operate. Probably something around or just over 24 deg. would be max. curvature for a NG 2-8-2.
Incidently, bridge and rail loading would have been worse with the engines weight on just 4 axles vs. 6, so I doubt weight was a factor, just the curvature.
