Why do the orbits of smaller bodies (e.g. comets and dwarf planets) have higher eccentricity? Larger planets eg. Earth, Mars $( e< 0.01 )$ have almost circular orbit, whereas orbits of  smaller planets like Pluto ($ e \approx 0.25 $)
  and smaller entities like comets have much larger eccentricity ($ e \sim 0.9 $).
Is there any reason why very small bodies have larger eccentricity?
Once something is in its orbit, its eccentricity does not depends on its mass (depends on the initial energy and angular momentum). But does mass statistically play any role determining the eccentricity when multiple bodies are formed, say, due to a collision?
 A: Eccentric orbits increase the probability of collisions or at least strong interactions between bodies, due to short distances at times, what change their paths. 
Bigger bodies have bigger mutual interactions in this case and are more affected. If they never get much close, what can be achieved by circular orbits, the system is more stable in the log run.
A: 
Once something is in its orbit, its eccentricity does not depends on its mass (depends on the initial energy and angular momentum).

This is only true in the case of the two body point mass problem. Add another body, or add an asymmetric body, and all bets are off. Small objects are much more subject to gravitational perturbations from planetary-sized objects than are other planetary-sized objects.
While the planetary-sized objects in the solar system long ago ejected most of the solar system's small bodies, that process is not yet complete. Jupiter and Neptune, and to a lesser extent and Saturn and Uranus, continue to perturb the orbits of the small mass objects in the outer solar system.
A: Orbital eccentricity e is given by:
$$\sqrt{1+ \frac{2EL^2}{\alpha^2M_r}}$$
Where, $M_r$ is the reduced mass. This establishes an inversely proportional relationship with the mass of the planet which is in our frame of reference. Hence making the eccentricity lesser with increasing mass. 
Another reason that I think would affect the eccentricity is the fact that if you consider the vacuum to be a space-time continuum then, the more the mass of the object, the more "bend" would be observed in the continuum. Imagine the planet as a ball on a sheet of cloth. Heavy ball would result in  a deeper cavity on the continuum and hence affect the orbit around which anything revolves in a similar manner and hence affect the eccentricity in a similar way.
You can imagine the way in which it would affect anything henceforth.  
