How would a person under gravity observe a person on a nearby planet but under 1000 times of that gravity? So, imagine I am standing in a region in space where the gravity is, say 1g. Now, on a nearby planet, there is my friend who is under the influence of much stronger gravity, like 1000g. According to Einstein's theories of relativity, gravity plays an instrumental role in time dilation. If I hold a stopwatch and my friend also holds a stopwatch, then after 1 year (in my frame of reference) if my friend throws his stopwatch at me, I would see that my stopwatch shows that only 1 year has passed but his stopwatch shows that less than 1 year has passed. This is because of the sharp bending of the space-time fabric near my friend's standing point (which dilates the time) but not as sharp for me, since the influence of gravity is different on both of us. I understand this. I also understand our minds are not capable of visualizing the 4th dimension i.e. time.
But what do you think how would I observe my friend during this 1 year of time (in my frame of reference). I mean would I observe him doing all the tasks in a slow motion? Or will his actions be quicker than mine? Or I will observe him doing things exactly as what I would observe a person who stands under the influence of the same 1g gravity as me?
 A: The relative rates of proper time for different stationary observers depend on the gravitational potential they find themselves in.  The gravitational acceleration experienced by these observers is the gradient of the gravitational potential.  So telling me that Observer A experiences a gravitational acceleration of $g$ and Observer B experiences a gravitational acceleration of $1000g$ is not sufficient to answer the question;  it's entirely plausible for one observer to be at a smaller gravitational potential but experience a greater gravitational acceleration, and vice versa.
If we do know the gravitational potentials $\Phi_A$ and $\Phi_B$ of two stationary observers*, then it's actually fairly straightforward to determine the relative rates of time dilation for each observer.  If two light pulse are emitted a time $\Delta \tau_A$ apart according to observer $A$, and received a time $\Delta \tau_B$ apart according to observer $B$, it can be shown that
$$
\frac{\Delta \tau_A}{\Delta \tau_B} = \sqrt{ \frac{1 + 2 \Phi_A/c^2}{1 + 2 \Phi_B/c^2}} \approx 1 + \frac{\Phi_A - \Phi_B}{c^2}
$$
From this equation, we can see that if $\Phi_B > \Phi_A$, then actions performed by $B$ will appear to be "sped up" when seen by $A$ (since $\Delta \tau_A < \Delta \tau_B$).

*The caveat here is that talking about "gravitational potential" only really makes sense in the limit where gravity is relatively weak. (A fuller answer is possible, but requires a lot more knowledge of general relativity and wouldn't add much more insight.)  Thankfully, gravity is "relatively weak" in the necessary sense for pretty much every compact object in the Universe except for neutron stars & black holes.  I disclaim any and all responsibility if you try to do such experiments near a neutron star and get the wrong answer.
