Christian culture regards all of humanity (or, in the more up-tight versions of the religion, all Christians) to be brothers and sisters. (This does not imply a literal common parent, but rather a spiritual kinship.)
The use of "sister" to refer to an unrelated woman is certainly not practiced extensively in most of the (white) US, but the term is used in that sense in some religious sects, particularly in the US South. And, while I have little first-hand knowledge (and Urban Dictionary is useless here), I've been led to believe that the use is common in certain African-American subcultures.
Using the terminology in Star Wars, in the fashion it was used, would tend to re-enforce the sense that the speakers are members of a common cult or culture -- I don't think there's any deep hidden significance.
In (British) English, a painlessly idiomatic usage would be
Mechanic: Do you want to repair your car?
You: Yes, but please don’t go overboard.
As thefreedictionary points out, ‘go overboard’ literally means falling out of a boat, but idiomatically one can also go overboard on a task: ‘to do too much; to be extravagant’.
That can mean a range of things, from taking a task in general more seriously than it could possibly merit, to polishing thousands of tiny details that no-one could possibly ever see.
In the case of your example, the not going overboard scenario would involve the mechanic simply fixing the essential problem efficiently, and stopping there.
John’s colleagues would understand each other perfectly if one of them were simply to say, ‘John is going overboard again.’ They might or might not try to stop him, but they would understand that John is expending unnecessary time and effort, as usual.
Best Answer
I believe that suspenders when worn by men are what are called braces in British English. Hence we have the expression belt and braces, applied to a course of action in which the participants wish to be doubly sure. Maybe this is what you have heard. It is not necesssarily applied to either a man or a woman.