This question is really hard to answer as it is, without knowing what your invention is, and what the other patent is about. But, after drafting this in comments, I've come to the conclusion that we might be able to lend at least a bit of insight to help you.
I think the best way for us to be able to help you, if this answer isn't sufficient, would be if you could post a new question with the patent number you're looking at. We'd then be able to give you an interpretation of its claims, to give you a more solid idea of what it actually covers.
Now, in thinking about the differences between something produced at macro- versus micro-scale, it's worth noting a couple fundamental aspects of the patenting system.
Claims are key.
As a result the application of the preexisting patent on the cm scale would make most of their embodiments and claims unfeasible.
If you clearly understand the claims of the previous patent or application, and they are solely dependent on the original scale of the invention, you can pretty well stop reading right now, and you should be fine.
A patent is only as good as its claims, so if they're for something other than what you're going for, it's pretty well irrelevant.
You can't patent an idea.
Section TL;DR: If the implementations differ enough between varied scales, you're probably alright, depending on the patent's text.
You can only patent an invention, or in other words, an implementation.
To extend your example, I can't patent "a way of holding water," but I might be able to patent "a water-tight cylinder with one closed end."
The difference here is fairly subtle, but you can imagine it more in a more serious case, of, for instance, a (looking at the thing in front of me), keyboard backlight. If I wanted to get a patent on my keyboard's backlight, hypothetically of course, I couldn't file an application claiming "a means to illuminating the keys on a keyboard." Rather, I'd have to claim something like "using a light source, from an LED or other form of illumination, mounted underneath individual keys on a keyboard." Neither of these are perfect examples, but they illustrate my point.
An invention needs utility to be patented, and to have utility, it needs an implementation. On top of that, patents need to be enabling, and to enable someone, you need something to enable them to do.
Now, that speaks to your situation, and exactly what you mentioned.
In your second paragraph, you talk about the differences in implementations between a bigger and smaller cup. Because the implementations differ, it's conceivable that the oppositely-sized version might not fall under the same patent.
Back to my point, though, you might still have some options. Consider your own example of a large cup being comprised of a collection of smaller ones. That might be patentable, in its own right. Because the implementation is novel and has utility, it could theoretically be patented.
Patents give a negative right.
Section TL;DR: If your implementation at a larger scale has improvements or special aspects to it, you might be able to patent those, even if the other patent still applies.
Looking at your situation from another angle, it's good to think about what specifically patents do for the assignee.
A patent doesn't give you the right to perform your invention, it gives you the right to stop others from doing it. That's called a "negative right."
What does that mean? Let's look at another example.
Say I hold a patent on a chair: "four legs and a seat." You come along, then, and you invent a way of making that a bit more comfortable. You file for a patent on "putting a pillow on top of a chair."
Now things get interesting. You can't perform your invention without infringing on mine, and I can't put pillows on my chairs without infringing on yours. That's often when "cross-licensing" deals come up, but that's out of the scope of this question.
Speaking from this approach, the fact that someone may hold a patent on the oppositely-sized version of your invention may not hinder your own patenting.
Looking back at your example of compiling a large cup from many smaller ones, you might be able to get a patent on that, even in light of the previous patent on a cylinder with a closed end. If you did that, you wouldn't be able to start creating those cups, but you might gain some leverage in licensing deals to be able to.
Ultimately, as I've said a few times now, it really just comes down to the claims of the previous patent. It could go either way. If the patent claims something as broad as "a water-tight cylinder with one closed end," that doesn't depend on size, so you might be blocked without licensing. If the patent claims something more specific to the implementation at some given scale, then you might be alright.
In situations like this, the best solution is often to speak with a patent professional, disclose your invention and the other patent you found, and get a professional opinion on what your best course of action might be.
In addition to, or perhaps even instead of, that, I really would suggest, if you're comfortable with it, posting a new question that provides the patent number and asks for help understanding it. Patents are notoriously difficult to write, and can be difficult to fully comprehend in reading as well. So if you aren't completely certain you understand it, I'd definitely leverage our community here to help.