My yoga instructor says that it is very important to practice balance poses because as we get older balance becomes a problem for many.
Weight has a very large impact on how we recover from a stumble. If you don't believe that just strap on a 50 lb pack and then practice a few stumble recoveries. You still have the same reaction time and you are not very much older from the time before putting on the pack but it is much harder to recover from a stumble. To carry this experiment a little farther put on ankle weights and wrist weight to simulate increased weight of the limbs.
I also think that added weight will not affect your static balance. What I mean is that if you are standing still you could stand there and be perfectly balanced as long as your legs would hold you up. There are plenty of obese yoga instructors that can hold balance poses that most skinny people would not be able to do.