This is a quote from the Wiki:
Think about it: If, through the laws of inertia, a heavier mass has greater resistance to being moved, why should gravity accelerate both an elephant and a book at the same rate towards the earth?
Take a look a the following video:
Basically what this is saying is that since there is an inertial mass and gravitational mass equivalence the book and elephant will always fall at the same rate. The equations are easy to see and I don't like to 'reinvent the wheel' so I just gave a link to the video. The bottom line is: Acceleration is independent of the mass according to the equations so it doesn't matter what the mass happens to be, it will always fall at the same rate.
Another quote from the Wiki:
To the rationalist the above experiments might appear to be futile, but to the empiricist, the fact that one mechanism is observed and not others is grave. While the proposed mechanisms of "graviton puller particles" and "bending space" versions of gravity in Quantum Mechanics and General Relativity, which Scientific American describes as 'whooping coincidence', provide equivalent, if absurd, explanations to the results of the above experiments, those things are completely undiscovered and unobserved, and so, are decidedly less empirical
There is no doubt that some of the proofs of gravity are hard to measure and are subtle. That alone does not make them less valid. Imagine yourself alone in a swimming pool. Focus your attention very, very intently on the level of the pool. Now empty your bladder into the pool. You know for an absolute fact that the level of the pool has just risen. Can you measure it? You would need very sensitive instruments to get a good reading. There would be plenty of noise. But if you did the experiment 1000 times and got a average reading wouldn't it give you a pretty good idea of the volume of your bladder?
That's the problem faced by many scientists trying to measure gravity under certain conditions. The theory matches the experimental evidence so the experiments are done many, many times. You eventually end up with an average of the readings and you use that as a good indication that your theory is correct. Why should that be a problem?