Genome-wide association studies (GWAS) have identified many disease-associated variants, yet mechanisms underlying these associations remain unclear. To understand obesity-associated variants, we generate gene regulatory annotations in adipocytes and hypothalamic neurons across cellular differentiation stages. We then test variants in 97 obesity-associated loci using a massively parallel reporter assay and identify putatively causal variants that display cell type specific or cross-tissue enhancer-modulating properties. Integrating these variants with gene regulatory information suggests genes that underlie obesity GWAS associations. We also investigate a complex genomic interval on 16p11.2 where two independent loci exhibit megabase-range, cross-locus chromatin interactions. We demonstrate that variants within these two loci regulate a shared gene set. Together, our data support a model where GWAS loci contain variants that alter enhancer activity across tissues, potentially with temporally restricted effects, to impact the expression of multiple genes. This complex model has broad implications for ongoing efforts to understand GWAS.