Why did Newcomen engine cylinders need to be enormous, sometimes exceeding 60 inches?

To generate sufficient force solely from atmospheric pressure acting on the piston.

Since the working stroke relied entirely on the weight of the atmosphere pushing down on the piston after a vacuum was created, the absolute force generated was proportional to the surface area of the piston exposed to that pressure (about 14.7 psi). To lift the heavy water rods and associated beam structure from deep mines, a tremendous downward force was necessary. To maximize this atmospheric force without increasing internal pressure, the designers were compelled to build cylinders of massive physical dimensions, sometimes reaching diameters greater than 60 inches. This necessity dictated that early industrial power infrastructure prioritized sheer material size over refined engineering.