A brother shares 50% of his genes with his siblings, the same amount as he would share with his own offspring. Genes responsible for caring about a younger sister are almost as fit as the genes responsible for caring about the offspring. But don't forget, every big brother shares 100% of the genes with himself, thus his own survival is twice as important as that of his brothers and sisters.
We are humans, we may become intelligent, but while we are kids, to a very large extent our behaviour is hardwired in our genes - the society still hasn't cut down on them. Most supposedly cruel actions stem directly from our wish to acquire more parents' attention for ourselves (as long as our siblings do not suffer at least twice as much because of that). So stealing candy from your small sister is natural, picking at her is natural, breaking her toys is natural, punching her is natural, provided that you don't hurt her too much. Logically, when there is significant age difference, your sibling is sick, etc., you switch to protection and support.
Not surprisingly, your siblings are in the same position. Thus your younger sister would be as nasty and vile as she can, provided that she is not punished and does not hurt you really much.
Inspiration: "The Selfish Gene" by Richard Dawkins