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Antibody folding and aggregation are major challenges in the development of relevant reagents and therapeutics. Antibodies face a biophysical trade-off; the immense diversity in complementarity-determining regions (CDRs), which is crucial for broad antigen recognition, comes at the cost of folding stability. How CDR sequences influence antibody folding remains poorly understood because of their sequence diversity and lack of large-scale data. Here we develop a high-throughput 'deep loop profiling' approach to quantify folding fitness across millions of diverse CDRs. Machine learning models trained on this dataset predict folding propensity directly from sequence and identify interpretable residue-level rules that reveal CDR1 and CDR2 as key folding determinants. Using these insights, we rescue two unstable nanobodies, including an aggregation-prone SARS-CoV-2 binder and a G-protein-coupled receptor-targeting intrabody, and build next-generation synthetic libraries enriched for biophysically optimized nanobodies. This approach provides a scalable framework for understanding and engineering folding competence in antibody-based scaffolds.