I was in a similar situation. I just returned from a trip where we did some challenging hikes and I lugged along my 70-200II, 24-105 and 5d markIII. It was a very heavy load but I am used to being a pack mule. For me, there is no question about the stunning beauty that I obtain from the 70-200. I switched back and forth with the 24-105 and after looking through the photos, the 70-200 has distinct advantages in quality that especially showed up when I was shooting in medium to low light. The quality difference narrows when you have good light but is still there. I decided that from now on I am using the 70-200 as my primary lens in spite of the weight
I just sold my 70-200 f4 (non IS) and although I enjoyed the photos it took, they really don't have the same quality as my new lens. One caveat is that the IS version might be a bit better than the non IS version. I was also very fortunate to buy the 70-200II barely used for $1700 and was thus able to justify the purchase. If money is not a big concern, then you would probably be happy with the lens. I would not buy it if it were to stretch your budget.
Regarding the one extra stop, for me the advantage is in the additional autofocus boost and for really low light. Having a 5d III has resulted in not needing to worry about low light as much and instead having to worry about too narrow a depth of field. Ironically enough, I found that I like setting the aperture at 4.0 for general shooting because when you fill the frame with your subject, the depth of field is significantly different than with the APS-C. However, when I have time to carefully compose the shot or when I am not filling the frame, I have used the f2.8 for great effect. With a 7d the extra stop will be more significant for lower light, your center focus point will be more accurate, and you will likely find yourself using f2.8 most of the time because your depth of filed isn't going to be as sensitive to mistakes.
Canon 5D MarkIII 24-105 F4 L IS | 100 F2.8 macro| 85mm 1.8 | 70-200 F2.8 L IS MK II | TS-E 40mm 2.8 | 50mm 1.4 | 20mm 2.8 | 300mm 4.0 L IS