How strong is the gravitational stretch we experience from the edge of the universe? How much gravitational effect do we experience (e.g. maybe -.00001 G or smaller) from the edge of the visible universe?  By edge of the visible universe, I am talking about the region of the cosmic microwave background and beyond.  In the past, the universe was very hot and dense, and we are seeing the light from this time period as the Cosmic Microwave Background.  It took slightly less than the age of the universe for that light to reach us, and it has become extremely redshifted with the expansion of space.  Since gravity apparently travels at the speed of light, we should be experiencing a gravitational effect from this shell around us as well.  As I understand, the universe was extremely dense back then, and it is around us in every direction, which would intensify the gravity greatly.  However, it is extremely distant, which would weaken the gravity greatly.  I don't know if redshift would affect gravity as it has the light from the cosmic microwave background, but if so, this would weaken the effect greatly as well.  With all this in mind, I am curious, what would be the effect of gravity from the edge of the universe on us?

Note: I would expect this to be a very small outward effect in all directions, something like -.00000001 g or something like that, but not 0.
In the past, the universe was very hot and dense, and we are seeing the light from this time period as the Cosmic Microwave Background.


This statement is (partially) correct. 
However....


  Since gravity apparently travels at the speed of light, we should be experiencing a gravitational effect from this shell around us as well. As I understand, the universe was extremely dense back then, and it is around us in every direction, which would intensify the gravity greatly.


This statement perhaps indicates that there are some misconceptions about the present state of the universe and also about what Cosmic Microwave Background Radiation really is (emphases added to identify the problem areas). So, in order to give a reasonable answer to the question asked, it would require addressing these misconceptions too.



The Big Bang model suggests that everything we see in our Observable Universe was once all concentrated in an infinitesimally small, hot and dense region of space. However, the Big Bang happened everywhere, which was followed by a super-luminal expansion of the space by a process called Inflation. The universe remained too hot still for any photons to roam around freely. It wasn't until the next 380,000 years that it continued to expand and eventually got cooled enough for the first hydrogen atoms to form. This is when the light first became visible. The remnant of this light is what we now now call Cosmic Microwave Background Radiation.

Again, it's important to note that the space was expanding in all possible directions continuously when the first light was emitted everywhere. In other words, the "dense" region from which the spacetime had begun, had now become comparatively much less dense overall. All through these years, this expansion hasn't stopped and every region where the light was first emitted, has now receded to great distances (46 billion light years in any direction). All the regions have cooled down further still to evolve into stars and planets, galaxies, clusters and any other celestial objects imaginable. 



So, to answer the questions asked (for simplicity, we'll stick to CMB as the "edge").... 


There is no space outside our Observable Universe which is surrounding us as a concrete shell. To be precise, it is merely a limit to how far back into the past and how deep we can peek into the space with our current technologies. Also, this has got nothing to do with the present state of the universe there. The universe is homogeneous and isotropic — meaning, you could go to any other place in the universe and it would still appear the same as it does from here — stars and galaxies everywhere.  Your vantage point would determine which galaxy appears as a distant blob to you and which region of space would merely appear as a CMB radiation. 
The regions which we now see as CMB, 46 billion light years away, are indeed one of the farthest reaches of space from where anything, including gravity, would have had any effects on us. By now, everything that we see as CMB would have coalesced to form celestial objects. But, there's a catch.... Remember, if the Sun was to disappear from the Solar System now, it would still take approximately 8 minutes for the Earth to be set free from its orbit. Meaning, the state of the Sun 8 minutes ago determines what gravity we feel because of it now. 
So, to compute the gravitational tug from CMB (46 billion light years away), we need to look at the state of the matter from 13.8 billion years ago minus 380,000 years (when the CMB was emitted). We can roughly assume that, back then, it was just Hydrogen atoms all over. The overall mass of all those atoms combined would have been equivalent to the mass of the Observable Universe, i.e. $10^{53}kg$.  
But again, the CMB was emitted everywhere and the isotropic nature of CMB tells us that departures from uniformity are only up to seven parts in a million! Meaning, when the CMB was emitted 13.8 billion years minus 380,000 years ago, the mass of the Observable Universe was distributed almost perfectly uniformly in every direction possible. From the distance of 46 billion light years then, this translates into almost equal gravitational pull from everywhere that light (and gravity) has reached us since then. Hence, the gravitational effects of the matter that is (i.e. was) spread uniformly in a radius of 46 billion light years from us, would be equivalent to what one would feel if they were to somehow reach the center of the earth — i.e. experiencing a nearly perfect equilibrium, with a net force of zero. 




PS: Should there be any discrepancies above, I'd wholeheartedly welcome the suggestions on correcting or improving the answer.