Heavyweight fighters are more susceptible to knock-outs. It's why heavyweight fights sell better than lightweight fights. Fans want to see a knock-out.
Heavyweights generally hit harder than lightweights, because they have more muscle and more mass behind their punches than lightweight fighters do.
When they're being punched at, heavyweights are slower to move out of the way and therefore get hit more often. Heavyweights tend to be slower, because they have more mass to move around, which requires more energy. And they have more muscle to keep oxygenated, which causes them to run out of breath. This means they tire a lot faster than lightweights in general, and that means they move slower.
When heavyweights are punched in the head, their head is generally more "attached" to and weighted down by their body. So their head stays more solidly in place and therefore absorbs more of the energy of the punch. Whereas, a lightweight fighter's head bounces off of the punch more easily. Both heavyweight and lightweight fighters' heads do this, but to a different degree.
Not to mention heavyweights are bigger and present bigger targets that are more likely, therefore, to be hit.
I found this interesting link which discusses some statistics from the UFC:
It reports that of the lightweight division fights, 25% ended by knock-out. Whereas of the heavyweight division, 61% ended by knock-out. And this trend can be drawn through each division. As the weight increases, so does the likelihood of a knock-out.
So this is all shaping up to be a real concern for heavyweights, isn't it? Not necessarily! It turns out that lightweight fights tend to "go the distance" more than heavyweight fights do. That means lightweights fight more rounds than heavyweights do. More rounds means they have a greater opportunity to get hit in the head.
In that same link, we see that lightweight fights went the distance 47% of the time. Whereas, heavyweight fights went the distance only 20% of the time.
So unfortunately, we can't conclude anything from these statistics regarding which division gets more concussions and/or brain damage.
Consider also that these are just professional fight statistics. That doesn't tell us anything about what happens during training. Fighters put far more time into training than into their fights. And one of the things that we're starting to hear more of from professional MMA fighters is that they're getting hurt from training more than their actual fights. They're starting to spread the word that sparring during training should be light. Too many MMA fighters go heavy during training, and they just end up hurting themselves (and their partners).
Personally, I believe even "going light" is enough to damage your brain, if it is repeated often enough. But I have no data to support that.
Children are especially at risk, by the way. Their skulls and brains haven't fully developed. They should not be hitting each other in the head at all. There are even studies showing that "heading" in soccer (football) causes problems for children: