 Solution

Use incident counts $Y_{it}$ divided by that village-year's population exposure $P_{it}$, and graph $r_{it}=1000Y_{it}/P_{it}$ against calendar year. Show separate small panels or labelled lines for all villages; a population-weighted overall line answers a different question from an equally weighted average village rate. A plot of counts alone can mistake population change for a rate change.

For the two printed villages, the observed rates per thousand residents are approximatelyThe first trajectory increases throughout; the second falls initially and then rises sharply. The last-to-first rate ratios are $1.472$ and $1.711$, respectively. The figure displays these two observed trajectories only. The other thirty village trajectories cannot be drawn from the PDF, because their observations were supplied in the separate emailed dataset.