large or small family

Can we say if somebody has just one sibling, he/she comes from a small family; if he/she has 2 siblings, he comes from a medium-sized family. However, if he/she has more than two siblings, he comes from a large family?

Possibly, but not necessarily. It depends on context.

In some places there are joint families with two or three generations under a single roof. You could have no siblings and still be part of a large family.

Also, "family" doesn't always mean the people you live with. It can also mean all your close relatives. You can be an only child living with just your parents and still be part of a large family if your parents have many siblings and they have many children and everyone's close to each other.