The issue of checking weight of carry on bags is simple

Overhead bins have a max weight limit.

Do you want overweight bags in the bin above your head when the plane crashes?

Do you really want that weight to be the cause of your demise?
If the bin breaks and the bags come down, it very likely will kill or at the very least incapacitate passengers. Who then if they survived the impact are incapacitated by someones excessive carry on.

Ask yourself if your carry on is more important that your life?