Ah, engineering tests. Are you sure you want to know?

Well, there are tests that measure rolling resistance at various tire widths. This graph shows how rolling resistance varies by tire width when tires are inflated to recommended pressures (wider tires = lower pressure). These tires are Continental Grand Prix 5000, the de facto standard low rolling resistance road tire:


Source: bicyclerollingresistance.com

The graph shows that rolling resistance changes very little with tire width, and wider tires have ever so slightly lower resistance, but since the difference is so small, that's one thing everyone can stop worrying about regarding wider tires.

The other factor is aerodynamic drag, where wider tires are at a disadvantage to narrow tires. You can make up for this disadvantage somewhat by using wheel rims optimized for a wider tire. Most of the modern carbon aero wheels are optimized for wider tires, starting at about 28mm.