Why did engineers start designing planes with aluminium skin on the wings instead of fabric covering? While the force of lift acts on the skin, to my knowledge it is not subject to high stresses
Wings and fuselages are subjected to twisting loads as well as bending so they need to be torsionally stiff. Prior to aluminum, the options were to make the wing/fuse with a frame of spars and ribs with fabric to provide the aerodynamic contours, braced with struts and/or wires to provide the torsional stiffness as well as resistance to bending, or, to do away with the struts and brace wires and make a monocoque structure (like an eggshell) with a plywood skin to provide torsional stiffness (with the spar beam inside for bending). If you wanted to go fast, you had to do away with all the bracing so plywood monocoque was the way to go.
When "duraluminum" came along after WW1, it was realized that as well as replacing sitka spruce for spar beams and ribs, it could also replace plywood for a stressed skin monocoque structure. You could build an airplane in the 1930s using plywood stressed skins bonded to wood ribs and spars, or aluminum stressed skins over aluminum spar beams, and have pretty much the same performance. You could make your egg about of plywood, or aluminum sheet, and it was pretty much the same egg.
There were so many manufacturing and durability advantages to aluminum (no glue, no wood rot etc etc), it was a no brainer to switch, once the metallurgy started to become understood well enough to use it as an engineering material, and plywood skinned wooden airplanes faded quickly.
I would assert that the breakthrough occurred when aluminum became (relatively) inexpensive to extract from ore on industrial scales. There was also a psychological factor, in that the popular american football coach Knute Rockne died in the crash of a Fokker passenger plane with a wooden wing when it came apart in a storm. All-metal construction then became a selling point for airlines.
Principally to carry greater loads. The skin on the wing forms an integral part of the wing box, which provides greater structural rigidity. It also provides better aerodynamic characteristics under loads. For instance Boeing has a particular way that it designs its wing scans, which is a proprietary secret, that causes them to flex when under load for better aerodynamic qualities.