I know it's heavy, blooming heavy! I've got one!
However, going from a crop sensor to full frame, I found 400mm just didn't cut the mustard any more. That left me with either the Tamron or Sigma 150-600 options.
I started out with the Tamron, it's actually quite a good lens, not too bad, did the job. Took it to Canada and took it on some hikes, got a few good shots:
Eastern Kingbird by
Chris Moody, on Flickr
Least chipmunk by
Chris Moody, on Flickr
North American beaver (Castor canadensis) by
Chris Moody, on Flickr
So yeah, light is a bit of an issue. But one other benefit of going full frame, is you can get away with higher ISO. That beaver shot is at 3200, and was taken at dusk in very low light. I raised the exposure in post processing to bring it back to daylight levels. Yes if you look at it 100% there's noise, a stock agency likely won't take it, but it's still useable.
Yet for some reason I decided, that despite getting a good number of keepers, the Tamron wasn't for me. I traded it in and ended up with the Sigma 150-600mm Sport edition. Given that even the lens hood is metal, it's a good kilo heavier than the Tamron, and I seriously doubt I'd have been able to lug the Sigma around and up through the Rockies like I did the Tamron.
However, weight is the only real downside... autofocus is very reliable, the build quality also is nuts, so I know the lens will last me a good long while. To answer the question about needing the light for the motorsports, and if you're thinking the subjects in the above shots were stationary, the following weren't exactly slow movers, and were even photographed in this country in October last year, where the daylight isn't necessarily that great:
Curlew by
Chris Moody, on Flickr
Kestrel with cricket by
Chris Moody, on Flickr
And this one was stationary, but it shows the detail obtainable:
Ruff by
Chris Moody, on Flickr
So all in all, on a full frame that does well in low light / high ISO, the smaller max aperture isn't too much of an issue. I'd be curious what Binary has to say about the noise on the 7DMkII compared to the 7D, which I found to be exceptionally bad.