Smallest, lightest tow on the ground you can buy in the U.S. today is SmartForTwo from the Mercedes division of Daimler. You have to decide whether that meets your transportation needs.
Type 1 Volkswagen from 1940s to 1970s was just a light and might be more useful (four seats). Indeed, most of the 4-seat subcompact imports (and some 2-seat sports cars, Lotus Seven weighed only 800 pounds) for the 1960s were lighter than the SmartForTwo because they lacked all the extra safety and ease of use equipment now mandatory for automobiles sold new in the U.S. My 1965 Renault 8 was actually lighter than the VW of the same year, and got about 10 mpg better mileage.
But realistically, you don't need a 1200 pound tow, you can readily tow almost anything under 3500 pounds (which covers most modern subcompacts and some compacts) and you can probably tow 5000 pounds, which gets you into mid-size sedans (but maybe not SUVs).
I'm towing a 2500 pound Honda Fit, about the smallest class of car you can buy here with 4-5 seats. Before that I towed a 3500 pound compact pickup truck. Nissan and Scion (Toyota) sell similar size MPV, and a Fiesta hatchback comes close, but when I was buying in 2012 the DFit was the least ugly car it its class. I looked at the next size up, but a Focus hatch equipped the way I wanted it was 600 pounds heavier and cost $7000 more.
The vehicle you tow has to first meet your transportation needs. That might not be the smallest and lightest available.
Tom Test
Itasca Spirit 29B