Spider-Man in the original timeline had a powerful longing for fatherly love. After Uncle Ben died, the guilt in his heart amplified his yearning for his father several times over. It just so happened that Stark entered his life then. The two got along exceptionally well, and their relationship was somewhat like that of a godfather and godson.
This timeline was different. Uncle Ben had not died and worked every day as a caregiver at Green Lawn Nursing Home. Whenever he had the chance, he would give Spider-Man an earful over this or that. Uncle and nephew had their conflicts at times, but overall, life was fairly pleasant. Peter Parker was more than capable of being filial to his uncle and aunt; there was no need for him to go looking for a godfather.
The current Spider-Man had not connected with Stark. Instead, because he lived with Mr. Fantastic in the Baxter Building, the two had developed a good relationship. Spider-Man admired Mr. Fantastic's immense knowledge and all sorts of wildly imaginative ideas, while Mr. Fantastic also valued his talent highly. Their relationship was somewhat half teacher, half friend.
After hearing the whole story about the West Coast Avengers, coupled with his natural fondness for Stark, Spider-Man hesitated for a while before joining the team as well.
There was also one uninvited enforcer in the process: Black Widow.
To be honest, Stark did not trust Black Widow. Her reputation was one factor; her unfathomable personality was another.
He considered himself well versed in human nature, yet Black Widow was one of the few people Stark could not see through.
"Which country's intelligence agency sent you to investigate me?" Stark's opening question was anything but friendly.
Black Widow's smile was a weapon. Smiling radiantly, she paid no heed to his hostility.