Right, it is not independent and it depends on the space and the object how the gravitation behaves. the smaller the space in which an object is located, the more or less gravity affects it, of course it also depends on the size and mass of the object. If we have an unimaginable big/wide open space and only one football, then this football will not really bend the space. But if the space is as big as the loading area of a pickup, then the graviation/gravity of the football will bend the space on the loading area of the pickup more clearly.