That's definitely nice to know!
You have already ruled out the portable lenses, a 70-200mm f/2.8 is portable, sort of, but its size and weight are all out of proportion to a 60D.
I'd suggest you consider a 70-200mm f/4L if you are going to carry the lens / camera around with you, or at least rent one and try it. It is large!
i find the 70-200 f2.8L ISII plenty portable i have the tripod foot removed which makes it feel alot nicer to shoot with just keep the foot stashed in the bag in case i need it. Good thing is the same foot fits this lens and the 300f4L so i just keep the 1 foot in the bag and have both lenses without the foot.