Crop yields must increase to address food insecurity. Grain weight, determined by grain length and width, is an important yield component, but our understanding of the underlying genes and mechanisms is limited. We used genetic mapping and near isogenic lines (NILs) to identify, validate and fine-map a major quantitative trait locus (QTL) on wheat chromosome 5A associated with grain weight. Detailed phenotypic characterisation of developing and mature grains from the NILs was performed. We identified a stable and robust QTL associated with a 6.9% increase in grain weight. The positive interval leads to 4.0% longer grains, with differences first visible 12 d after fertilization. This grain length effect was fine-mapped to a 4.3 cM interval. The locus also has a pleiotropic effect on grain width (1.5%) during late grain development that determines the relative magnitude of the grain weight increase. Positive NILs have increased maternal pericarp cell length, an effect which is independent of absolute grain length. These results provide direct genetic evidence that pericarp cell length affects final grain size and weight in polyploid wheat. We propose that combining genes that control distinct biological mechanisms, such as cell expansion and proliferation, will enhance crop yields.