Upward. As you stand on the earth, you feel a force pushing up on the bottom of your feet that's indistinguishable from standing inside a spacecraft in deep space far from any planet or star while a rocket engine under your feet accelerates you in the direction of your head at 9.8 m/s^2.
This is Einstein's "Equivalence Principle" at the heart of general relativity (GR). He assumed this was true and then worked out all the implications. One of those implications is that time passes more slowly in an accelerated frame relative to an inertial frame, and this has been demonstrated experimentally many times.
The atomic clocks on the global positioning satellites appear to run faster than atomic clocks here on the earth because we're being accelerated by gravity to a greater degree due to our lower altitude. That's "gravitational blueshift". At the same time, an observer on a GPS satellite comparing the local spacecraft clocks to time transmissions from clocks on the earth's surface would see the surface clocks appear to run faster than the local spacecraft clock; that's a gravitational red shift.
This is distinct from, but related to, the time dilation from special relativity (SR) that applies to observers in different inertial coordinate systems, i.e., in which all the observers feel "weightless". It also resolves the famous "twin paradox" from SR, in which an astronaut who flies rapidly away from the earth and then returns will be younger than his twin who stayed behind even though during the coasting phases of flight both perceived their twin's time as passing more slowly than their own. The reason is that the astronaut twin had to accelerate to achieve his high departure velocity, then he had to accelerate again to cancel that velocity and create a high velocity back to earth, and then the effects of GR kick in.
Note that in space flight, the effects of GR and SR are often in opposite directions, with one (usually GR) dominating; that's the case with GPS. On earth, GR is also easier to demonstrate with atomic clocks than SR though both have been done. It's easier to just go up a mountain and wait for a while than it is to maintain a high velocity relative to the earth.
Einstein did something similar when he derived special relativity (which he did before general relativity). He made a very simple assumption that the speed of light was exactly the same in every inertial reference frame regardless of the relative velocities of source and observer. And then he followed that to all its logical conclusions.
This is all pretty mind-bending, but both SR and GR are firmly supported by mountains of experimental evidence. That's the difference between real science and pseudoscience; real scientists will accept all sorts of weird and seemingly counter-intuitive things provided they're supported by the evidence.
