Jacking one side does not (significantly) stress the tires on the other side; there isn't much if any weight transfer there. You're just taking the weight that the tires on the side you're jacking up off of those tires and putting it on the jack.
There is a very tiny bit of weight transfer due to the angle of the trailer shifting and so its center of gravity being ever so slightly closer to the other side, but it's no different than parking on slightly sloping ground...or walking from one side to the other in the trailer.