I've heard nothing but good things about Sigma lenses and I don't see why whatever difference there is between the Canon and the Sigma (except for $2000) would be significant for wedding videos shot on DSLR.
I agree that lenses are worth the money, but only when there is some specific quality to a lens that you want and can take advantage of. I wonder if the difference in quality between the Sigma and Canon would be as noticeable in video, after the loss in resolution and the compression, compared to still images...
For now I'd say do more research and maybe even tests before you buy, if possible. Use it in similar conditions and with a similar style that you'd use for the wedding photography, and do that in video mode. It might even come down to how it handles and feels. I know of lenses that have given me good images but feel plasticky and light and I can't manually focus in the way that I want to, and that's been a bother.
But there are very detailed reviews online, which may suffice, that also cover how the lens feels and handles.