Why do most airliners have underwing engines, while business jets have rear-mounted engines?
Underwing engines have more advantages for larger planes, but there must be enough room underneath the wing to mount them. 

This was tested by Boeing in the 1960s, when they designed the B737 and had two competing teams pre-design both configurations. The underwing config won. When Airbus designed the A320 two decades later, the underwing config won again with engines that were a good amount wider.



Image source.

Advantages of underwing mount:


Engines mounted in pods underneath the wing reduce the upward bending moment of lift creation, and therefore allows for lighter construction. 
If the pods stick out forward of the wing, the backwards aerodynamic twisting moment is also reduced: lighter construction.
The engines can be easily reached for maintenance.
All of the fuselage can be used for useful load - tail mounted engines have structural reinforcements in the fuselage between the engines.


Advantages of fuselage mount: 


The yawing moment of a single engine fail is smaller, allowing for a smaller vertical tail.
Fuselage can be lower to the ground and allow for low door sill height.
Landing gear can therefore be shorter.
Clean wing configuration.
Lower trim change due to thrust.
Less noise in most of the cabin.


In smaller planes, the wing bending &amp; twisting moment is a relatively smaller constructive issue than in larger planes. And indeed, being closer to the ground allows for easier boarding via air stairs.