one thing, none of these lenses mentioned are "light". they are all over a kilogram and you WILL feel them in your hand/arm
especially if you're coming from cheap telezooms.
70-200 f/2.8 L is a fantastic lens, constant & fast aperture, but you will add an extender for your needs (soccer), that will slow down AF speed (which will reduce your rate of keepers) and lower the IQ a bit as well.
70-300L is great, maybe the best of the bunch (between those 3 you listed) for your needs, since it's the lighest, the most recent design, weather sealed, extremely sharp and has latest generation IS. but i can't justify it's cost for a variable aperture lens. and it's not a fast lens (f/4-5.6), so you'll need lots of ISO to stop action, especially above 200mm or so (the range you'll need most?).
100-400L has great reach and the zooming is different, it's a hate or love thing i think. but it's again not a fast lens so i pass...
i personally would go for a prime such as 300mm f/4 (since the f/2.8 version is way beyond the budget). you won't be zooming indeed, but once the action is in your viewfinder, it will deliver far better results (great IQ at that focal length with very fast AF). then you could save up for the legendary 300mm f/2.8 or even 400mm f/2.8 haha
good luck with your decision, i know it's not easy to decide :p