Regarding lens size and weight there is no substitute to testing this yourself.
I wouldn't consider any of the 70-200mm zooms too heavy for extended use. If for example someone can safely carry a baby, why wouldn't the same person be able to carry a 70-200mm f2.8 Mark II zoom on a gripped 5D?
This is, unfortunately, missing the point on so many counts.
1. Do you frequently hold up the baby at eye level, rather than resting him on your shoulders/body?
2. When you are also carrying other gear, food, etc., then the additional 1 lbs can be an issue.
3. Sometimes, there simply might not be room in the bag you are carrying, and you might not want to take a bigger bag for so many reasons (real-life experience).