A physical theory is just a mathematical model that predicts the evolution of the physical system it is describing. The more successful theories tend to be motivated by experiment, but this doesn't have to be the case e.g. string theory. Any theory can be proposed, but at the end of the day the test is whether the theory makes predictions that match experiment. The successful theories do match experiment, while the remainder fall by the wayside.
The problem with your idea is that it isn't well enough developed to make any predictions that could be compared with experiment. However one thing that strikes me is that it isn't obvious how your theory reduces to special relativity in the low mass limit.
Any theory of gravity has to reproduce special relativity because special relativity has been so thoroughly experimentally tested. In general relativity, agreement with special relativity simply means the low mass limit has to be the <PERSON> metric and it's normally obvious that this is the case. It's not at all clear to me how your suggestion would do this.
More specifically, GR is a theory of curved spacetime not just curved space, and in particular the manifold it describes has a signature of (-+++) and it's the negative sign for time that gives us all the weird stuff like time dilation and length contraction. 651
I see nothing in your suggestion that is related to this.
However the idea you describe isn't without connections to GR. If you take for example a stationary black hole and use Gullstrand-Painlevé coordinates the metric can be written in the form:
$$ ds^2 = -dt_{ff}^2 + \left(dr + \beta dt_{ff}^2 \right)^2 + d\Omega^2 $$
where the parameter $\beta$ has the dimensions of velocity. The interpretation of these coordinates is that the radial coordinate is flowing inwards towards the singularity at a velocity $\beta$, and the observer is carried along much as you would be carried along in a river. Hence this is commonly referred to as the river model of black holes.
This bears some similarity to your idea that observers would be carried along in an expanding space(time?) but the resemblance is only superficial. For example why would the observer be carried along with the spacetime when the circles (the colliding stars?) are not. We know that all mass gravitates, but you seem to suggest that only high masses gravitate i.e. don't move with space. Presumably you would have some equation to relate an objects tendancy to move with the space as a function of mass, but you don't give any idea of what this might be or what its physical motivation is. 562