Short answer: ARSPD_RATIO is the adjustment for air density (rho) and linear pressure-sensor error.
In AP_Airspeed::read() (the method that reads the airspeed sensor) the formula for airspeed measurement is seen:
airspeed = .3*sqrt((raw_pressure_msmt - sensor_offset) * ARSPD_RATIO) + .7*(last_speed_measurement)
Breaking it down, we see there's a... "30% updated moving time-average filter" (That's my words, anyone know the technical name for this type of filter?) on the calculation.
From Bernoulli's principle we find that we expect airspeed to vary with the square-root of pressure, so that part makes sense.
So ARSPD_RATIO and sensor_offset are the "slope" and "y-intercept" parameters mapping the sensed pressure to what we believe is the actual pressure, and also accounting for the 2*rho constants in Bernouli. I think this explains why the initial value is sent near 2.