I started this as a comment to @Amadeus's excellent answer, but it kept growing and I decided to turn it into an answer.
One form of a weak female character is one that exists for men; is portrayed as, and acts as if, her only purpose in existing is to be pursued by men, to get married, to have children, to be sexually attractive to men or desired by men.
If a female character only talks to other female characters about men (finding men, understanding men, being rejected by men, being persecuted by men, hoping to be rescued by men, how to please men, or alternatively she only views other women as competition for men, to be defeated), OR about traditional "female" duties like children or housekeeping, she is not a strong female character.
I'm going to cherry pick two women I personally know, let's call them Ann and Zoe.
Ann lives to catch the perfect man, be the perfect mother-wife (while still working because 'status') and show off her perfect family and life. She talks A LOT about men, hair, clothes and jewels; she sees every other woman who as much as looks at her 'targeted catch' as an enemy to be humilliated; and her life seems to revolve around looking sexy and showing off how men pursue her.
Given the wrong perspective, Ann could be portrayed in a story as the poster child of the weak female character who lives to be pursued by men, especially because most of her conversations revolve around men and looking sexy for men.
Given the right perspective, she's a strong female character who has a purpose in life and works hard to achieve it. Does she have a shallow personality and acts like a bitch? Definitely. Is she happy? All the women I know who have also spent time with Ann swear she isn't. But being happy or having chosen a poor purpose in life doesn't mean Ann can't be portrayed as a strong character in a novel.
How can one show Ann as a weak or a strong character? One way is precisely through her relationships to other characters, especially female characters who are sometimes so fed up with her obssession, they call her out on it. Female characters who are either taken in by her show of grandeur, are suspicious of it or can barely put up with it for more than ten minutes in a row. Or female characters who see her for what she really is and either keep their distances or use her obssession to manipulate her.
These relationships would allow the reader to see how she works to achieve her purpose (and thus how she has agency of her own) and how, nevertheless, her world truly revolves around herself, with 'pursueing men' being merely a measure of her own success.
Ann may be seen as a 'weak person' by the reader, due to her choices in life, but not necessarily as a 'weak character'.
As for Zoe, she's the poster child of the traditional housewife, except that she has to work. Her world revolves around her children and her husband, she's one of the few women I know who shines with happiness at the prospect of having parties at home - and she prepares most of the food, she cleans it all up afterwards, and she's still beaming with happiness over the whole thing.
Given the wrong perspective, she's a weak female character who gives herself up for the sake of her family.
Given the right perspective, she's a strong female character who chose an outdated purpose for her life and who is constantly fighting to be the wife and mother she has always dreamed to be.
How can female relationships show that she is a strong character? Well, they'll allow the reader to see that if Zoe revolves around her husband and children, it's because that is what brings her happiness. Despite those friends who criticise her for putting herself last, who drag her away from her family for a girl's night out (and switch off the phone so her husband doesn't get the chance to play the hapless guy around their toddler).
Again, Zoe may be seen as a 'weak person' by the reader, due to her choices in life, but not necessarily as a 'weak character'.
The relationships shine a light on what makes the characters tick, on their wishes and desires. Even if they are fulfilling traditional, old-fashioned female roles, the relationships these characters have with other women allow the reader to see why they chose those roles and how they fight to achieve their goals. They do not sit and wait for things to happen, unless they see it is A) a proof of their power over their admirers, or B) a sacrifice they make to be what they think they should be.