Personal bag and carry-on

Hello,

I can't find anywhere if it's allowed to have a personal bag in addition to the carry-on luggage for domestic flights, would they allow me to have a laptop bag (my laptop is 15.6" and weighs 2.5kg so i would be well over the 5kg limit) in addition to my carry-on? Also do they systematically check the carry-on's weight? I've read they rarely or never do it if the carry-on luggage looks small enough, but i wanted to make sure!

Thanks in advance !