The Sustainable Development Goals (SDGs) of the United Nations provide a blueprint of a better future by 'leaving no one behind', and, to achieve the SDGs by 2030, poor countries require immense volumes of development aid. In this paper, we develop a causal machine learning framework for predicting heterogeneous treatment effects of aid disbursements to inform effective aid allocation. Specifically, our framework comprises three components: (i) a balancing autoencoder that uses representation learning to embed high-dimensional country characteristics while addressing treatment selection bias; (ii) a counterfactual generator to compute counterfactual outcomes for varying aid volumes to address small sample-size settings; and (iii) an inference model that is used to predict heterogeneous treatment-response curves. We demonstrate the effectiveness of our framework using data with official development aid earmarked to end HIV/AIDS in 105 countries, amounting to more than USD 5.2 billion. For this, we first show that our framework successfully computes heterogeneous treatment-response curves using semi-synthetic data. Then, we demonstrate our framework using real-world HIV data. Our framework points to large opportunities for a more effective aid allocation, suggesting that the total number of new HIV infections could be reduced by up to 3.3% (~50,000 cases) compared to the current allocation practice.