Laptop Tsa Briefcase

Carry-on, Laptop, AND Purse?
TSA says you can have on carry-on and one personal item (purse, briefcase, laptop, etc.). If I have a carry-on, and put my laptop in it in its own bag, then have my purse, too, would that be allowed? Also, two more questions: Are there weight limits on carry-ons? And what are the dimension limitations for purses/under-the-seat items?
I’m flying on American Airlines, if that’s makes any difference.
Oops! I meant if I put the laptop bag in my carry-on, and then have my purse, too.
You are allowed one carry on bag or suitcase and one personal item such as a laptop or purse. Put either the laptop or purse in your carry on luggage and you’ll be within AA’s limit for carry on baggage. You can’t have a carry on suitcase, a laptop and a purse, the laptop and a purse are two personal items and youj can only have one. Here’s AA’s webpage for carry on allowances:
http://www.aa.com/i18n/travelInformation/baggage/carryOnAllowance.jsp
Mobile Edge Element ScanFast Briefcase