Why are motor capacitors huge in physical size even though their values are in uF range?
Motor capacitors are not plain electrolytics, because the voltage across them reverses at the mains frequency. 

The larger value ones are start capacitors - usually bipolar electrolytic, and rated to the peak mains voltage - but not for continuous operation. They are usually disconnected by a centrifugal switch in the motor, which operates when the motor is up to speed. Consider that not only is the voltage high, and continually reversing, but the ripple current is high too (especially when the motor is still at low speed) and you'll see the apacitor has to handle unusually high power.

Smaller value ones (10s of uF) are used as run capacitors in smaller (less than 1hp) motors. These phase shift the current to the start winding, but remain connected during operation, so must be rated for continuous operation. These are usually film capacitors (or, if old enough, paper in oil) which are much larger per microfarad than an electrolytic.