As mentioned previously. It's a static load. You're not going to hurt the tire or rim if it's just sitting with additional load on it, over its rated capacity.
Maybe other reasons to block both tires...soft ground, less flex or sway when using the camper, but that's negated by dropping a couple of the camper jacks to stabilize.
The following is copied from Page 124 of the Michelin Truck Tire Service Manual:
HERE"When using blocks to level motorhomes or RVs,
extreme caution must be taken to make sure the tires
are fully supported. The weight on the tire should be
evenly distributed on the block. And in the case of duals,
it should be evenly distributed on blocks for both tires.
If not, the sidewall cables can become fatigued and
damaged, resulting in a sidewall rupture and a complete,
sudden loss of pressure.
Note in the correct method, the blocks are wider
than the tread and longer than the tire’s footprint. This
provides maximum support to the tires and assures that
the load is evenly distributed."
There's also some pictures that illustrate the Correct and Incorrect way to use leveling blocks.
Quite a difference than some of the opinions given in this thread.
Taking proper care of your tires is a major safety factor, that may involve yor life and well being.
ryoung