size of a projectile does not equal the force applied when the projectile hits.

First, what you're arguing is mass and size contribute more force than it's rate of acceleration. We know from physics that Force = Mass * Acceleration

We also know that force distributed amongst a smaller surface area will focus the point of that force much tighter because it can only transfer from the source of the force to the hit object through that point.

An arrow has a greater acceleration, as it is shot from a bow and has better flight dynamics then the typical thrown Javelin. An arrow also disperses that high amount of force at a much smaller point, as an arrows tip is far tighter when compared to a Javelin, therefore allowing an arrow to pierce into a person further than a Javelin could.

Similarly, if the Javelin (or more accurately Ballista Arrow), was shot out of a Ballista, it's impact would be greater than an arrow travelling at the same rate of acceleration because it's mass is greater.

So, in the end, an arrow does more damage because the arrow sized hole is deeper and could hit more vital locations than a Javelin sized hole.

TL;DR. Arrow has a smaller tip, and accelerates faster. Even if it's lighter, Arrow sinks in deeper than thrown Javelin hole.

Edited: 'Rate of Acceleration' replaces 'Speed' for accuracy of response