Does space have an elastic quality?
What I was thinking about was if space is expanding, is it being 'stretched', like a balloon being blown up, and if so, is this causing gravity to weaken? Imagine space as a 2 dimensional sheet (got this from one of Brian Greene's books) with planetary bodies resting on it and causing a depression in it, if you were pulling this sheet from all sides over a period of time, you would cause the depression of the planetary body to decrease and eventually become flat, which if we go back to reality, would mean that the gravitational 'constant' had changed to the point where the planetary body had no influence on those objects which were previously orbiting around it (or even residing on it's surface).
Is this the case in reality? Or does space not have an elastic quality? If not, can you explain to me what exactly it means for space to be expanding?
In case you didn't notice, I'm a layman (hence the Brian Greene books :p), so try to keep your answers/explanations conceptual if possible.