I think officially many airlines in the world have such a restriction. Many do not enforce this rule. EVA just does it - it used to be they would have people walking around the gate to check if the carry ons are too heavy and make you check them. I don't know why they enforce this - if you think about it, it is a safety issue and they are entitled to do this.

Years ago, I went on BA C from LHR to SIN. They forced me to check. Guess what? When I got to SIN, my bag did not make it.