The "tennis anyone?" phrase is used to describe someone who is rich and doesn't work; instead, they hang around the country club looking for people to play with. Rich and aristocratic people are usually taller than workers (better food!), so this is another symbolic description. The girl in your example is clearly someone who comes from a family that has been rich for many generations.

The tennis-anyone" refers to the phrase: "Tennis anyone"? You here that a tennis clubs when someone wants a game of tennis and doesn't mind who he plays against. So he asks: "Does anyone want to play tennis?" Or better: "Tennis, anyone?" I suppose it refers to a tall girl who is very sociable, or doesn't mind who her "opponent" is, and can easily hold her own in any conversation.