Over the billions of years that the Earth has been orbitted by the Moon, its rotation has slowed by the slight resistance to the tide as it travels round the planet (relative to the Earth of course, it would appear static relative to the Moon).  The tide is of course caused by the gravitational pull of the moon and the equal and opposite gravitational forces of the Earth and the Moon keep the Moon nicely in orbit around the Earth.

As the force causing the braking effect of the tide is exerted by the Moon's gravity, there should be an equal and opposite force to the braking that is being exerted on the Moon.  As the tide is working as a brake on the rotation of the Earth, it would be expected that the bulge of tidal water is slightly ahead of the Moon with the Moon's gravity pulling it back.  I suspect that this bulge slightly offsetting the Earth's centre of gravity out of line with the Moon's centre of gravity and the Moon's centre of rotation might have some such effect.

Admittedly the effect would be rather small, but over the periods of time such as the time it has taken for the Earth's rotation to change from 6 hours per day to 24 hours per day surely there has been some effect.  If so, am I right in thinking that the Moon's orbit has quickened over time?  If so, I hope the Moon has stayed in equillibrium by adjusting its altitude (is that the right word?) and isn't thinking of leaving us to it once it has built up an escape velocity...

I have a theory that may work in conjunction with popular belief that dinosaurs were wiped out by meteor impact. Given the size of animal and plant life during the time and to some the seemingly laughable proportions ie huge bodies and small legs arms of some creatures. If gravitational strength was lower those creatures would not need strength in proportion to body mass or wieght.  Plants would/could grow larger taller without the confines of gravity as we know it. Could it also explain the seemingly impossible feats of strenth we debate over regarding placement of objects and the building of structures by our human ancestors. Scientists research and tell us of THE meteor impact that wiped out the dinosaurs. Could it be that over a period of time there was more than a couple of impacts that we can no longer find evidence of and that, and by changing the density and mass of the earth we now experience gravity at a higher strength. We know that physically we adapt ie loss of hair due to temperature change, creatures in caves being blind etc.