Here is something to consider also. The Sony lens selection for the new E mount full frames are still in their infancy and what is available is no bargain that is for sure. There isnt a ton of cheaper third party lenses out yet for that system which makes it even harder. That's the main reason I didn't make the switch, as tempting as it was. Sure you can use an adapter and even use other lens but then what you lost in size and weight is just made up with the adapter. Plus there is loss in focus speed and fstops. How much video do you do in low light, minus HHN? You can always look into some sort of lighting for your camera, a lot of options in that department that wont break the bank
If money is an issue here is what I would do
Stick with the Canon, get the 80D and then maybe lens or 2, would still come in cheaper than just the Sony body alone.
If money wasnt so much an issue
I would consider even a Canon FF, you're looking for better low light performance and that should give you a little bump up in low light shooting. You would need to figure out which lenses you have now that would be compatible with a Canon FF to see what you would need to get rid of. 5D Mark III perhaps? Another option is the 6D which is FF and about the same cost as the 80D
If money was no problem then all in with the Sony lol. I want to get the new A99II but right now its more than i want to spend and making the jump to the A7 put me in the same spot you are in. Go price out the A7 you want and all the glass you'll need, its insane.
I know carrying around more isnt something you really want to do but another options is getting a separate dedicated video camera that shoots great in low low light. You can probably swing that plus the 80D and a lens and still be cheaper than just the Sony body lol