Understanding what contributes to cross-national differences in public health spending among low- and middle-income countries (LMICs) can help identify how policy-makers can reduce global disparities. Yet, research on this topic has so far overlooked the potential influence of one of the most strongly recommended economic reforms during the post-war era: reducing international trade taxes, 'tariffs'. Tariffs are an important source of tax revenue for some LMICs. Tariff declines can impact on government finances, and these changes may constrain public health expenditure where states lack the capacity to tax non-trade activities. We examined the association between tariff changes and public health spending in 65 LMICs, 1996-2015. We identify substantial variation in this association according to one indicator of state capacity, a country's score on the World Governance Indicators government effectiveness (GE) index. For example, tariff declines corresponded to reduced public health expenditures in countries with low GE scores. Our results suggest that tariff changes and domestic taxation capacities have an under-recognised impact on public health expenditure and may contribute to global health spending disparities.