I fly EVA PE a lot and yes they weigh my hand luggage all the time and put a tag on it. Then I show them my laptop case and they say no problems and never weight it. I do not think EVA is that strict with the carry on but as other have said I have seen a lot of stuff that I was surprised that got through check in and even the gate coming on to the aircraft.
ON the other hand Cebu Pacific would not let me take my hand luggage saying it is too heavy. Why it was heavy was I had put my jacket inside. So I had to remove the darn thing and wear it until I got through security and then put it back in my hand luggage. Cebu Pacific was checking just before you go to immigration and security.