I hope this might help. I own the a7R, the 70-400 mm G zoom, a SLT a77, and the full frame adapter (LA-EA4) and have had to chance to work extensively with them. To cut to the chase, I do not use the 70-400mm on the a7R with the adapter, but simply keep that long zoom mounted on the a77. Part of the reason is convenience. I dislike changing a big lens out in the field and if I am carrying such a large heavy optic, it is simply more convenient to have it mounted on the body ready to go. The weight penalty of having to carry second camera body is made negligible by the size and weight of the zoom.
Having said that I have used the LA-EA2 adapter and it does involve some light loss. It uses 1/3 f-stop of light for the auto sensor and the remaining 2/3 f-stop goes to the sensor. Its size and weight is not big--it weighs 4 ounces and it works nicely on the a7R. I use this adapter with a Tamron 90 mm macro and a 100-300 mm APO Minolta Zoom and I have no complaints of about using it with either. Basically, focusing speed is on par with my a77. For these two lenses, I will use the LA-EA4 adapter as both are reasonably compact and the both are excellent optics. I might add that even without image stabilization, these two lenses are usable with careful hand holding techniques. It might be just me, but I prefer using the 70-400 mm on a tripod--but then again, I just turned 65 and I am getting a tad weaker. A friend is trying to get me to buy his 1.4X Sony Teleconverter to use on the 70-400 mm. He reports it is optically good; however, the lens will not autofocus with this adapter. I am on the fence about buying this as it will make the 400 mm the optical equivalent of a 800 mm lens (on an APS-C sensor) and I do not know if I need a lens this long. By the way, the 70-400 mm is a wonderfully sharp and I enjoy using it on the APS-C sized sensor cameras.