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It's the mass of the lens that matters, not just the weight. The mass and how it is distributed along the barrel determines the inertia/momentum (mostly the angular type), and hence the agility of the lens.
Yes, and 200-400L is just too heavy for intense action where handheld use becomes imperative. Even 500 II is too heavy. The venerable 400 f/5.6 prime is much more suitable, and so is 400 DO and even 300 f/2.8 IS (assuming there is good proximity to target)
200-400L is almost as long as the 500, and going by its block diagram, it looks like it could be fairly nose heavy, which is not favourable when it comes to the control of lens swings, as well as the necessary physical effort.
Db, those are respectable looking shots, and the little heron in flight is quite a catch.