I shoot Nikon and have no idea about Canon.
But the weight difference of Tamron's 70-200/2.8 (1500 gr.) and 100-400 (1135 gr.) appears to be a bit more than only 200 grams...
I also like to add, although I could use the 200 mm extra range, I mostly pack the 100-400. Needs less space and is (on APS-C) sufficient to do these shots: https://sojujo.smugmug.com/Testshots/Tamron-100-40045-63/
But the weight difference of Tamron's 70-200/2.8 (1500 gr.) and 100-400 (1135 gr.) appears to be a bit more than only 200 grams...
I also like to add, although I could use the 200 mm extra range, I mostly pack the 100-400. Needs less space and is (on APS-C) sufficient to do these shots: https://sojujo.smugmug.com/Testshots/Tamron-100-40045-63/