Why did Arthur and Molly Weasley not join the original iteration of the Order of the Phoenix, during the First Wizarding War? We know that they were definitely old enough to join (it is stated in the Goblet of Fire that the Whomping Willow was planted after Molly left Hogwarts, and we know that it was planted in Lupin's first year).
So why did Arthur and Molly not take part in the original order, and its resistance against Voldemort?
There is no direct canon information (books, interviews, pottermore that I checked).
However, by the time Harry's parents were murdered, Weasleys already had 6.5 kids (F&G were 2 years ahead of Harry, Ron was same age, Ginny 1 year younger). Wikia gives the date range as
Bill was born in 1970, which is approximately when the war began, and Ginny was born in 1981, two months before the end of the war
Having 5-6-7 small kids to raise kind of puts a damper on most people's most activities, be it social life, or participation in secret orders.
Building on @DVKs answer, JKR has confirmed on her own website that Gideon and Fabian Prewitt (both of whom were members of the original Order of the Phoenix) were in fact Molly's older brothers:
"No one lived after he decided ter kill 'em, no one except you, an' he'd killed some of the best witches and wizards of the age — the McKinnons, the Bones, the Prewetts.
Although there's no canon confirmation one way or another, it's a distinct possibility that they were instrumental in Molly not becoming a member of such a dangerous organisation, basically vetoing their baby sister from joining.
We see a similar occurrence in the books, with Molly seeming to bar Ron, Harry and Hermione from becoming full members.
