You don't necessarily need to drive slow. Remember that you get better mileage on the highway than in the city. You need to drive steady, and I suppose accelerate at a decent amount.
New cars are getting lighter, not heavier. They are always looking at getting lighter materials for the body.
My 1990 Protege was 2300 lbs, my 2005 Corolla is 3200. Both have about the same sized engine, both manual tranny and both got/get a combined 32mpg around town with the AC on being driven by both a sedate mom and a leadfooted dad.
My pigmobile T&C with a 3.8l V-6 got 22mpg on a 3000 mile roundtrip to Colorado from Texas last year and clocked in a 16mpg roundtrip up Pikes Peak. Getting 20 around town by coasting a lot.