why do some maintain the 24-70 given the cost?
24-70mm is generally the most used focal length (general purpose focal range) for most people ... but that may not hold true for some people ... but majority of my photos are usually made with that focal length ... I suppose that is the reason why "some maintain the 24-70". Having said that in your case, since you already have the 24-70, and as others have already recommended, the obvious choice is to get the 70-200mm ... unless if you would like make a lot of ultra wide angle images, in which case you would want to get the 16-35 L or the 17-40 L.
although the weight has been mentioned as being prohibitive (particularly as a travel lens). i struggle to understand how 860g versus 1500g can really come into the equation??
If you are calculating 860gms vs 1500gms, it does not sound like much, but you have to remember that you also have to carry your camera (5D MK III) that weighs 860gms (body only, without battery) ... on your travels you obviously would not carry only the 70-200mm lens, you would also pack in your 24-70mm lens + a bag + spare batteries, maybe a filter or two and what not ... when you add all that up you are talking about carrying at least 3500gms (maybe even 4000gms all day) ... now I don't know about the weight being "prohibitive" but carrying 3500gms - 4000gms all day (not counting any other items such as your iPhone, iPad, water bottle, snack etc) does not contribute to a lot of fun especially during your travels. Having said that I did carry my 24-105 f/4 L IS & 70-200 f/2.8 L IS II during my vacation to UK, I carried the combo for 2 days and gave up (due to the added weight), from the 3rd day onwards I only carried the 24-105 for the rest of the holidays.