It draws 44,000 hits from Google, so it is by no means moribund, though nowadays not so common and it may be frowned upon. The meaning is clear. Answer says it has to do with a weak member of a group. Not sure how they came up with that angle. I see it as a comment on character. “Twisted sister” could be its (or her) progeny.

Wonder why specifically a sister. Sister city, sister stud (strange enough, along with a cripple stud), things are sistered on to, etc. Brothers don’t get the same treatment. I guess for the same reason a ship is a she. How old might the phrase be?

It may very well have an origin in the phrase ‘weak brother’ or brethren, but there are some gaps in the pedigree.  While Tindale in 1526 has “And so thorow thy knowledge shall the weake brother perisshe for whom christ dyed”, it’s not until 1857 that there’s an American citation using the feminine version, “‘weak sister’ and a rather ‘bad egg’”.  A bit dodgy, I’m afraid, but both do refer to persons of questionable or unreliable character.

There may be some relation to sob sister, first cite 1912. The cite for sob-brother is interesting too in that it couples it with weak-brother.

1914 J. LONDON Let. 23 Sept. (1966) 430 All I can say is that he is a weak-brother, a sob-brother.

1912 Sat. Even. Post (N.Y.) 7 Dec. 9/3 Of the Daily Blatt’s seven sob sisters six had husbands; and of the six it was more or less pure coincidence that five were supported by their wives.

more or less pure coincidence

That would be an example of an understatement, and in the tradition of understatements, say no more.