Lightest new car today is the Smart for Two, considering your two-passenger requirements. It is a computer shifted manual transmission, but that you are not likely to notice the difference between that and a traditional automatic.
A number of sub-compact imports from the '50s and '60s will have been lighter, and four passenger, but will almost always be manual transmission, and not have air conditioning, power steering, power brakes, power seats, power windows, et al, and if they have a sunroof it will likely be fabric and you will move it by hand. At two-passenger, you might have been as light as 800 pounds empty (smaller versions of the Isetta).