How would one use the Android accelerometer to measure one's mass? Pretty much what the title states. 

The Android CDD says of the Accelerometer


  
  MUST be able to deliver events at 50 Hz or greater
  MUST comply with the Android sensor coordinate system as detailed in the Android APIs  (see [ Resources, 41])
  MUST be capable of measuring from freefall up to twice gravity (2g) or more on any three-dimensional vector
  MUST have 8-bits of accuracy or more
  MUST have a standard deviation no greater than 0.05 m/s^2
  


So I find myself wondering - would it be possible to measure one's mass by taking a short hop with the device strapped to chest/waist? The raw accelerometer data would provide the duration and acceleration encountered on both upward/downward leg (pun unintended) of the hop.
Newton's second law states that Force = Mass * Acceleration.  We can use this formula to solve for Mass:: Mass = Force / Acceleration.  As such, we need a known force in order to take a measurement of acceleration to determine mass.  Hopping into the air is going to be a variable, instantaneous force.  Also, your legs are going to act like variable force springs to absorb your impact with the ground.  All of these variables would really frustrate your attempt to get anything close to a valid mass reading.

NASA has created device that uses the measurement of acceleration to determine mass for astronauts in space.  The Space Linear Acceleration Mass Measurement Device (SLAMMD) uses two springs to generate a known force on the subject and then reads the acceleration to determine mass.  There is a nice video on YouTube explaining how it works and providing a demonstration of the device in action.