The only way a difference in weight of SAAMI Spec cases could make a difference is case volume. That extra weight has to go somewhere and it goes to the inner volume of the case. A little bit of difference in case volume can make a significant difference in pressure.
I expect that cases of the same volume would perform the same regardless of weight or head stamp.
True, but not the whole story. Rim thickness, bevel, and extractor groove depth are variables which do not affect internal volume.