In The Godfather Part II, at some point during the events in Vito's past, his child was sick.
In the book, there is no implication that Fredo is of below average intelligence but in both The Godfather films, Fredo is pretty clearly slow and in more than one scene behaves not just "weak" but frankly dumb. Vegas when he suggests a clueless solution to Michael's disagreement with Moe.
So for sure, the movie has Fredo as, compared to his siblings, being the least of them intellectually.
Was the sick child indeed Fredo? He was the oldest, so that is pretty clear. Did the director decide to show us that Fredo as an adult suffered yet from childhood illness, and here's reason that just occurred to me: FFC himself had polio which of course sure did not effect his intelligence but must have been a powerful force for shaping his own psyche.
Actually, I read that Sonny was the oldest and if there was no older kid in the household, it was Sonny who was sick. So probably I am wrong about this unless we saw a young Sonny and an infant Fredo in The Godfather 2.