Guiding Principle: everyday expectations
Our guiding principle here, the RAI, comes from a 2020 tweet by Jeremy Crawford:
In D&D, everyday things—walls, gravity, bread, laughter—work the way we expect them to, except for when the rules say otherwise.
For example, D&D has magical effects that pass through walls, for walls are assumed to be impenetrable, unless you damage the wall itself.
Specifically referencing gravity, Crawford here says that we can expect it to work the way it does in our world, except when the rules say that it doesn't. In other words, sometimes the rules of D&D do not follow the rules of physics, but we will be specifically warned when they do not.
Turning to the Hand, we can find two references to how it moves in its description (emphases mine):
The hand lasts for the spell’s duration, and it moves at your command, mimicking the movements of your own hand.
Here we have the 'except when the rules say otherwise' part - the Hand can be moved by you up to 60 feet - this will not be affected by gravity (that is, you can move it sixty feet regardless of whether you are moving it up or down, it will not move faster if you move it down, unlike a normal object) and the Hand mimics the movements of your own hand. Your own hand, being an 'everyday' thing, is affected by gravity, and the Hand will mimic its movements. When you relax your hand, your fingers droop down, in the direction they are pulled by gravity, but only as far as their connection to your hand itself permits. Since the Hand is mimicking the movements of your hand, it will respond to gravity in a similar way - not because it is itself affected by gravity, but because your hand, which it is copying, is.
For the 'way we expect them to' part, should the Hand, as an object, fall when you are not moving it, since we expect objects to fall? Personally, I read the "moves at your command" as "moves [only] at your command", where the "rules say otherwise" is here specifying that gravity will not, in fact, cause the Hand to fall. However, I recognize that this is my interpretation, and is not explicitly RAW. For someone (perhaps the OP) seeking stronger evidence, let us assume that the hand will be affected by gravity - will it fall? What is our 'everyday expectation'?
As stated at the start, the spell specifically creates the Hand as an object, and ordinary objects fall. But the Hand is no ordinary object. Rather, it is an object made of "shimmering, translucent force" that "doesn’t fill its space". The fact that the Hand doesn't fill its space is important because it means that creatures cannot push against it. So, how would you expect an object made of force that doesn't fill its space and can't be pushed against to react to gravity? Would it fall? Would it drift? Would it re-orient?
I certainly don't have much everyday experience with such objects, and I expect most DM's don't. Thus, even for a reading of the spell that requires the Hand to be affected by gravity, it is completely unclear to me how it should be affected. This then becomes subject to DM ruling - the DM should decide how the Hand behaves in a manner that it consistent with other 'objects made of force' that exist in their world.