Your motor has two windings:start and run. The start is long and small diameter. The run is shorter and larger diameter. Length creates magnetism, diameter creates ability to take heat (created by amps). Start winding and capacitor creates the kick to overcome enertia of being stopped. The switch at about 2/3 speed kicks out the winding to keep from overheating the start and the cap. The run is always in the circuit and can take the heat of running. To have the start winding in at all times would require the motor (with larger windings) to be 50 to 100% bigger in physical size. The cap is filled with a salt solution and overheating will boil it and cause it to short.
As the switch gets dirty, burnt, or full of sawdust it keeps the start in too long which then leads to cap failure. Do not replace the cap unless you address the switch. If the cap is bad, the wax plug between its terminals will be cracked and there may be a salty, sticky residue. If the cap is not bad, it can bite you if it is still charged. It will not kill you, but it is not nice (I didn't know that my arm could move that fast!). The switch is inside the non-shaft end-bell. Take a digital picture before moving any wires. A good blast of air may be all it needs. However, a bad cap will usually have burnt contacts. File two or three strokes with a needle file, NO more unless absolutely needed. Or clean up with some 320 grit sandpaper, blow-out contacts after cleaning. The centrifical weight should have the contacts closed when still. Weight should pull against the springs and open the contacts as the motor spins up to speed and must move freely. This is not rocket science. Make reference marks at both end-bells before removing end-bell. Lining up those long bolts is very difficult without marks. When reassembling the motor, tighten the bolts in
at-least four steps. Spin armature after and during each step, light taps with a hammer maybe necessary. :icon_thum