We have a few inherited rolls of parafilm that have probably been overheated or perhaps oxidized (some have a brownish hue). I had taken some media out of the autoclave and got autoclave tape adhesive on a finger. Turned out to be a sneaky, sticky bonus when I went to peel a bunch of film strands.

No more tearing at a corner and ruining the whole piece! I'm sure it has other bonus features like dust accumulation, but it kinda made my day. Lab tape and "scotch" tape work just as well.

I've also tried putting it in a fridge to see if it would help the wax shrink from the paper, but didn't improve the problem. I've also recently read high v/v% ethanol makes them easily slide apart. Mine didn't exactly slide apart--the paper just tore in half--but it was significantly easier.