Fuel efficient vehicle for large people

I would look at the Nissan Altima and Hyundai Elantra and Sonata. They are reasonably roomy and fuel efficient by my standards. (Not sure what your benchmark is.)
Also, look closely at the differences in mileage between compacts and so called mid size cars like the Altima and Sonata. Often times the differences are not as great you might think. My 2001, 3400 pound V6 Lumina is practically a full size car, and I get 21/32 mpg. I keep a light foot on the gas and the engine feels to me like it is operating effortlessly most of the time, especially effortlessly at highway speeds. Plus it has big, wide comfortable seats and a heavy, solid ride that I like. They stopped making the Lumina in 2001, but if you don’t mind an older car, the Lumina and its sister, the Buick Century, offer wide comfortable seats and what I consider good-enough mileage. They also tend to be good values on the used car market because they are not nearly as in demand as the much more popular Asian sedans.