Ok, simple question:

 

Say I'm standing on the ground on Earth. I'm not moving, so I'm pushing down on the ground with a force of my mass * 9.81 m/s2.

 

Now, I jump straight up, and in doing so, I push on the ground with twice that force. Thus, I should accelerate upwards are 9.81 m/s2.

 

Would I say I'm "pulling 1 G" (based on my acceleration) or "pulling 2 Gs" (based on the force on the ground, including the portion supporting my body weight)?

you're pulling 2-g's until your feet leave the grounf then you'd be pulling zero.

 

it works on an absolute basis.

So a resting body on the ground is always pulling 1g?

Exactly -- and that is exactly what an accelerometer says. An accelerometer at rest on the surface of the Earth reads a constant acceleration of 1g upwards.