do they regularly make you weigh your carry ons?
Not as a rule.
However, a few weeks ago when I was on Concorde Room Door duty, a BAA security manager asked me about the maximum weight BA allows in the cabin.
When I told him that the official rule was as long as the passenger can lift it above his head, he chuckled. "That's no problem to this guy - he's in the US Marines! His trolley bag weights 42 kgs - are you really going to let him take that on board your Dusseldorf service?"
It turned out the bag had travelled in the cabin all the way from Dallas, full of parts to help restore a 1965 Mercury and he had packed it in the cabin bag bto avoid paying excess on his hold baggage. We got him to buy another bag and split he weight evenly between the bags, and then checked them in at the T5 Central customer service desk.
Kinda made me wonder, though, about what sort of weight is going in the overheads!