I own the 24-105L, 24-70L II and in the past I've owned the 24-70L. I also have a 28-135 that is my daughter's walkabout.
I love the 24-105L for the handy range and IS when I'm on vacation, and I tend to use it at f/11 a lot as it is my vacation lens where I am typically interested in large DOF. About the only thing I don't like about it is the distortion and vignette on the wide end.
The 24-70L II is superlative and if you can afford the high cost it should be on your list. The optical performance is really excellent and I use mine wide open a ton. I find myself using my 24L II, 50L and 85L II primes quite a bit less than I used to since getting this zoom. One other note about it is that this lens is similar to some of the other Canon recent 'L' zooms that it has a degree of focus accuracy that is noticeably better than I've experienced before. The new 100-400L II is another such lens. I have both and I can say that these lenses just hit focus dead on shot after shot after shot. I'm used to the odd inexplicable miss with my other lenses, and these generally just don't do that.
I have no experience with the Tamron or Sigma lenses. I typically only buy 3rd party EOS lenses when they offer a particular lens that Canon doesn't, like my Sigma 120-300/2.8. It's up to you if you feel like 24-70, f/2.8 and IS all together in one lens represents a unique package, and if so then the Tamron is probably your choice.
I don't personally think of any of these 24-XX zooms as being 'large'. To me a lens like a 70-200/2.8 or 100-400 is kind of large and my 120-300 is definitely large. But I'd have no problem slinging my 5D and 24-70 over a shoulder and wearing it all day.