I was raised being called "sister" by my family. What's the background on this usage?

I was called "sister", as a replacement for my name. (Oddly, my brother was not called "brother.") I never questioned this growing up in the 50's in a rural area. It says much about the culture I grew up in. Yet I cannot explain it well, to younger people or to those not from a rural upbringing, in the 50's and prior.

This was reflective of my role in the family, not any sisterhood. A friend was confused by this, only understanding sister as in sisterhood.

I haven't been able to find any background or etymology on any website. It's simple but I'm interested in cultural aspects as well as any fiction reflecting this.

In the Oxford English Dictionary, there are a full eight different senses listed for sister. For its use as a vocative, however, they write:

In the vocative, as a mode of address, chiefly in transferred senses. Also colloq. as a mode of address to an unrelated woman, esp. one whose name is not known.

1943 Amer. Speech 18 88 [New Zealand English] Sister is also used for a girl as a term of address. It is not‥a recent adoption from American films, but a relic of the whaling slang of a century ago.

The first use of sister as a vocative in any sense is from the 12th century:

c1175 Lamb. Hom. 5 Leoue broðre and sustre ȝe hi-hered hu [etc.].

In the specific case of calling someone sister as befits their position in the family, there are no notes of when it was first used. According to the OED, sister was first used around 900AD. As a vocative, this meaning could have transferred at any point after 1175. I cannot read Old English, so I am unable to tell if it contains the same use of sister as in your case.