Alitalia made me check my rollaboard once. Ever since then, when traveling with a companion, I let them hold, it while I check in with nothing but a briefcase, and vice versa. Without a companion, I try to hide the rollaboard (22" travelpro regulation bag) so they don't even ask to weigh it.
BMI was very strict one time at DUB. So I simply removed my water, books, and overcoat, took it back to her and it weighed ok. Checked in, went and sat down and filled the bag back up again.