Silly comments aside, "fat" wings, ones with greater camber, were all the rage 100 years ago when designers found they could eliminate draggy external bracing by building cantilever wings. Hugo Junkers was one of these pioneers.
Wind tunnel testing also showed increased camber not only increased lifting efficiency, but also, combined with large, rounded leading edges, produced very benign stalling characteristics. One result of this research, the Fokker D.VII., so terrified opposing pilots that it was specifically banned after the end of the "Great War".
Heavily cambered wing design such as the Davis wing lived on until aircraft began pushing the limits of the "sound barrier". Aircraft fly higher to get more speed with the same amount of drag, and this works great until the wing approaches its critical Mach number. Above this, drag greatly increases, ending the reign of the "fat wing".
Modern "super critical" wings, literally "surf" the slower bottom airflow, leaving the top of the wing as flat as possible. This is what airliners use at 35,000 feet.
But at 1000 feet, where airspeed is limited to 250 knots, the "fat wing" makes a comeback by deploying slats and some flap. For a given wing area and Angle of Attack, the "thin wing" is only more efficient when Critical Mach Number is approached.
This is why many airliners have a never exceed speed for lower altitudes, and a Mach limit for higher altitudes.