With that analogy, the balloon would be the ruler in my analogy, which leads me back to the original questions. Using the balloon analogy, if you have a normal balloon in 3D euclidean space, you can measure/define the expansion easily. Without that, what can you do?
You could define some physical process on the balloon as distance and time, like light moving and atoms vibrating, and call that our ruler. Then measure intrinsic properties like curvature? If hypothetically the speed of light instantly dropped by 5% (with respect to existing objects' distances, I guess), do you just define those objects as instantly 5% further apart now, or do you you say something like the speed of light changed? Then there'd be similar questions about changes in how we define time. This is fun to think about.
You could define some physical process on the balloon as distance and time, like light moving and atoms vibrating, and call that our ruler. Then measure intrinsic properties like curvature? If hypothetically the speed of light instantly dropped by 5% (with respect to existing objects' distances, I guess), do you just define those objects as instantly 5% further apart now, or do you you say something like the speed of light changed? Then there'd be similar questions about changes in how we define time. This is fun to think about.