It’s never a good idea to stack material, it can cause charring, and a even cause a fire in some materials.
So Step 1 is to stop stacking them together, and definitely never layer with different materials like posterboard. (You got lucky.)
Step 2 is to cut yourself a handful of these out of some scrap Medium thickness plywood or draftboard:
They are the absolute best thing for holding down flexible materials, and keeping it from bowing up while it’s being cut.
Step 3 is… the best way of dealing with the quirks of leather that I found is this info:
Step 4, last but not least: Run some tests using a small square on each piece of leather to see how it is going to cut and to determine the best settings…it’s not going to EVER be the same unless you are using Proofgrade. You will need to set Custom Settings.