It is a myth that the old leather footballs were routinely heavier than modern footballs - they were actually marginally lighter. However, they became heavier in wet weather as they absorbed water. But only a minority of matches are played in the rain.
I remember some neurosurgeon saying that it wasn't so much the weight of the ball, or even the force with which it was headed, which was the problem. Rather it is the movement of a (soft) brain up against a (hard) skull. Think of it like an egg in an egg box - the eggs don't break since they are snug and cannot move.
Obviously in football, the brain will move most frequently with headers, but in sports like rugby and NFL, the problem comes with big hits, where whiplash causes the brain to be jerked in all directions, even when there is no actual contact to the head.
I'd be interested to know what the brain damage stats are for goalkeepers. Similarly eg with orthodox wingers, who rarely head the ball, either in games or in training.