According to the WHO, in 2021, about 32% of pregnant women in sub-Saharan Africa were infected with malaria during pregnancy. Malaria infection during pregnancy can cause various adverse birth outcomes such as low birthweight. Over the past two decades, while some sub-Saharan African areas have experienced a large reduction in malaria prevalence due to improved malaria control and treatments, others have observed little change. Individual-level interventional studies have shown that preventing malaria infection during pregnancy can improve birth outcomes such as birthweight; however, it is still unclear whether natural reductions in malaria prevalence may help improve community-level birth outcomes. We conduct an observational study using 203,141 children's records in 18 sub-Saharan African countries from 2000 to 2018. Using heterogeneity of changes in malaria prevalence, we propose and apply a novel pair-of-pairs design via two-stage bipartite and non-bipartite matching to conduct a difference-in-differences study with a continuous measure of malaria prevalence, namely the Plasmodium falciparum parasite rate among children aged 2 to 10 ($\text{PfPR}_{2-10}$). The proposed novel statistical methodology allows us to apply difference-in-differences without dichotomizing $\text{PfPR}_{2-10}$, which can substantially increase the effective sample size, improve covariate balance, and facilitate the dose-response relationship during analysis. Our outcome analysis finds that among the pairs of clusters we study, the largest reduction in $\text{PfPR}_{2-10}$ over early and late years is estimated to increase the average birthweight by 98.899 grams (95% CI: $[39.002, 158.796]$), which is associated with reduced risks of several adverse birth or life-course outcomes. The proposed novel statistical methodology can be replicated in many other disease areas.