So I kinda went with the totems idea that was introduced in the comics. But the more I thought about it, the more I realized all species would have had totems that probably represented the best of that species. It was my thought that Peter might have carried with him the Human totem.
So... at some point the spider was experimented on and she got out and stayed at the university. She learned things about humans, their letters, their learning, ect. She had children, though not would retain the gifts she had gotten. She may have even been caught another time or two for experiments. Eventually she saw Peter and her instincts told her he should have her totem. He was worthy.
So she bites him not realizing she took his. As she began her transformation, it was the reverse of Peter's. She started off as a Woman-spider for quite some time before the process progressed and she became more human and ended up in Houston, TX for various reasons. Just as Peter held some spider instincts, she held his memories and words of his uncle Ben.... HER uncle Ben. She could remember both lives and both would guide her. Hr human powers amaze her. The things she can do now, as well as things lost, are bout beautiful and frightening to her.
She is Lady Weaver. She is Texas's protector. And she will wield the power of the human totem proudly.