I don't think they weigh carry-ons. They do frequently check carry-ons at the gate though.Do airports weigh check in bags? We have only done carry ons for the last 10 years or so. Pack them tight and use a pack back that is probably larger than you are supposed to have and you are fine for a week.
I know that I overpack. I spill a lot. Still, my wife's bag always weighs about twice as much as mine.