Cause of observed galactic red shift or acceleration in expansion of the universe: velocity vs gravity.

Scientist look out at the universe and observe red shifts for galaxies that are roughly proportionate from their distance from us and attribute it to a velocity away from us. Also there is an indication that the universe’s expansion is accelerating. My question is: Is or isn’t a proportion of the red shifting attributed to gravity on a cosmic scale?

Here is my argument. As we go back in time, the observable universe was smaller, and locally, more dense. When we observe a galaxy that is 10 billion light years away, we are looking at it with light that left it 10 billion years ago. Excepting large scale cosmic structures and voids, generally the distant galaxy’s local density should be roughly the density we had 10 billion years ago.

Now some might point out that from the perspective of that distant galaxy, mass distribution would be the same in all directions and would not effect photons emitted from that galaxy. But from our perspective, 10 billion light years into the future, we do see a mass distribution gradient. The photons that left that galaxy 10 billion years ago has gravity from in-front and behind working on it; that from our perspective, over its journey to us, it has collected more mass behind it than when it was first emitted, thus causing at least some of the red-shift we observe; that in a sense, it has climbed out of a gravity well.

Maybe I have it all wrong because I missed something. Maybe scientist already have factored this into their models. Or maybe I stumbled onto a something important that will change our understanding of the universe. Seeing as I am little more than a layman on the topic, I am inclined to believe one of the first two conditions probable likelihood. And, seeing as I am just a layman, a simple English explanation of what I missed would be appreciated. But if I am onto something, then maybe it might change our thoughts from the universe’s accelerated expansion to an apparent accelerated expansion.