Adding glue or doping or rubber cement affects the compliance. I looked at that pic and thought to myself...leave it alone. That dosnt look like anything you need to be concerned with in my opinion. You want equal forces on the entire circumference of that cone/suspension. Adding goop to the suspension in one spot will change that.
Personally I would smear a little bit of silicon rubber on both sides of the tear. Don't goop it on, but cover well.
You have to choose between 2 evils. Yes the added weight will affect the suspension a little bit.
HOWEVER the tear is acting as an air leak. And that may be more of an issue than a small change the the suspension.
Also if it is not fixed-there is a good chance it will get worse and be harder to fix later.
Of course the proper repair is to have it reconed-or possibly have a new surround installed.
But if it were my speaker-in the current condition-I would use silicon rubber and be done with it.