CPB,
You make sense, but there are still loose ends.
If you won't define Gravity as an acceleration, what is your understanding of what causes it?
What little understanding I have of general relativity talks of gravity a being a curveture of space-time, which governs the motion of inertial objects.
In other words,it talks exclusivley about acceleration, not force. Force is a consequence of the mass of the object and the acceleration due to the space-time curveture.
Thus, the response to "Why do you have weight when not accelerating" is that you ARE accelerating in curved spacetime. You consider us inertial while on the ground. GR considers us inertial while in free-fall, but NON inertial when on the ground.
Newtons laws can be used to calculate the effects of forces very accuratley, and in Newtonian physics, there can be no acceleration without force. What Newton does NOT do is explain WHY gravity does what it does. GR does, and it does indeed tret gravity AS an acceleration, rather than just a CAUSE of acceleration.