But what if we know that we can't measure the fall time accurately? What if we can only measure it to within an uncertainty of 80% or so? Then our belief isn't strictly falsifiable, but we can gather some evidence for or against it. In that case, would we say it pays some rent?

Yes. As a more general clarification, making beliefs pay rent is supposed to highlight the same sorts of failure modes as falsifiablility while allowing useful but technically unfalsifiable beliefs (e.g., your example, some classes of probabilistic theories).