One cause of childhood obesity is a reduction in the amount of unstructured time spent outdoors, resulting in less physical activity. Greenspaces have the potential to increase children's physical activity levels, so it is desirable to understand how to create spaces that promote visitation and activity. We investigate the relationship between rates of obesity at ages 4 to 5 and 10 to 11 in small-area census geographies, and indicators of the neighbourhood greenspace environment, in the northern English city of Sheffield. To capture the environment at scales relevant to children, we test the importance of overall green cover; garden size; tree density around residential addresses; and accessibility within 300 m of any greenspace, greenspaces that meet quality criteria, and greenspaces with play facilities. We use a multimodel inference approach to improve robustness. The density of trees around addresses is significant at both ages, indicating the importance of the greenspace environment in the immediate vicinity of houses. For 10 to 11 year olds, accessibility of greenspaces meeting quality criteria is also significant, highlighting that the wider environment becomes important with age and independence. More attention should be given to children's requirements of greenspace when considering interventions to increase physical activity or planning new residential areas.