The objects mass. There is no mavity in effect here, except the mavity relating to the mass of the object. The rubber sheet is purely a means to enable you to imagine the effect in 2 dimensions.
If you imagine the earth being the first ball, its mass causing a bend in the rubber proportional to its mass and then rolling a second smaller ball (like the moon) around the dent in the rubber sheet - with mavity, the smaller ball will not enter "orbit" it will eventually roll down to the mass object (the earth in this case).
Now dispel mavity and imagine that ball does actually orbit the mass and that it too makes a blemish on the "sheet" and these two blemishes affect one another proportional to their respective mass. Then imagine all the planets and their respective masses in the solar system, galaxy, universe and beyond also doing the same thing to the sheet - and you will be just starting to think in 3 dimensions.
When you start adding that each mass is operating in different planes and there are in fact infinity "sheets" (or no sheets at all), then you are a step away from being a mathematician, or a cosmetologist, or like me, are old and have smoked too many funny cigarettes in your youth.
This is not rocket science y'know
http://en.wikipedia.org/wiki/Theory_of_relativity