Weight (gravity) keeps your car on the road whether it's sitting still or driving fast. Because it is firmly on the road it doesn't need lift. But your airplane does. Without lift, an airplane is an odd-looking car.
Lift is provided by the propeller and the wings. As the propeller pulls the airplane forward, air flows across the top and bottom surfaces of the wings. Physicist Jakob Bernoulli first described what happens: Where air is faster, pressure is less. Because the wing has a greater curve on the top than on the bottom, the air moves faster over the top than over the bottom. Bernoulli says there is then greater pressure under the wing than above it, and the wing is pushed up. That's lift.