There was an article a while back in Quilters' Newsletter Magazine about a quilter who had had a stroke, so she was lacking in strength on one side of her body, she used heavy weights to hold a ruler in position.
When you say multiple layers, how many do you mean? How many layers can you cut before it's too many?
Have you taken other steps to make it as easy as possible, perhaps investing in a 60mm rotary cutter, the blades are expensive, but you can save it for when you really need it, rather than all cutting. Also, make sure you are cutting at the right height, on a good quality board, with a ruler that isn't working against you. Also, just depending on exactly what you are cutting, you can find that you need to exert more force on the ruler because only one small section of it is resting on the fabric, so sometimes it's helpful to places extra fabric, perhaps bits you've already cut to support the ruler, rather than trying to just press hard on one small area.
Have you tried using a rotary cutter with your left hand? I have on/off problems with my right thumb, so if I want to finish cutting, I have been known to set my rotary cutter up for left handed cutting and do it that way. There are several different types of rotary cutter out there, which have you use your hand at different angles, so I could get one that didn't require me to squeeze with my thumb, I just haven't got round to it, because it's not a problem all the time.
Cheers Anne