This is assumes the reader understands time dilation from gravitational redshift, and has a basic understanding of mechanics.  First, let me throw a thought experiment at you...

Set Up:

My UFO is extremely powerful, powerful enough to pull or push planets and even stars.   One day I found a dead star system with a small non-rotating black hole that has an event horizon radius of 1,000 km.  The system has two planets, A and Z.  In the outer orbit (r(Z) ~ 1.5 x 10^8 km), planet Z is aging at the same rate as an Earth clock.  Planet A is orbiting the black hole very closely (r(A) ~ 2700 km), and clocks on planet A age at only ½ the rate of a clock on planet Z due to time dilation from gravitational redshift predicted by the Schwarzschild solution.  I’ll use gamma=2 for this relative redshift throughout this post only for simplicity.

I use my UFO to pull planet Z, and accelerate it with a given thrust 1 m/s^2.  I fly in with my UFO and pull to accelerate planet A, also 1 m/s^2 with the same engine thrust I used on Z, so it is almost exactly the same mass as planet Z the way I see them locally.  So as measured locally, mass of Z = mass of A (Say both are 6 x 10^24 kg).  Now to simplify what is observed, I’m only pulling the planets in a perpendicular direction to the orbit radius (to avoid arguments regarding the radial contraction in the metric).  And to avoid relativistic complications from velocity, let’s slow the orbit velocities to a stop just before running each experiment.

At planet A, me and my saucer age slower relative to Z (by General Relativity’s gravitational redshift), and the whole acceleration process then appears to occur slower to observers on Z because of time dilation.  No big deal right?  But when I leave a line attached to A, fly out to Z, and then try to pull A: I can only accelerate it about 0.5 m/s^2 with the same engine thrust I used before.  Planet A feels twice as heavy (accelerates half as fast) to my UFO when I’m pulling it from the Z orbit!  Why?

The Paradox:

If we break down acceleration, we find it is dv/dt, or a change in velocity over a change in time (the differential limit is where the changes approach infinitely small).  And velocity is just dx/dt, or a change in distance x, over a change in time, so acceleration is dx/dt^2.  Now the units are what are important.  Since the change in time at Z is twice the change in time at A because of time dilation, the acceleration at A when viewed from Z appears to be only 1/4 of the local acceleration, assuming the distortion of the Schwarzschild geometry (in time only).  To paraphrase: When viewed from planet Z, the UFO is near planet A and appears to pull it only a quarter of the acceleration that is measured locally.