In the 2002 Spider-Man, the character played by Tobey Maguire explores ideas for what his costume will look like and what symbol he will use. One of the options that Peter Parker rejected was the Black Widow’s emblem, another Marvel Comics character: the red hourglass, slightly modified in the movies but still recognizable.
By the way, fans have a theory as to why Spider-Man’s costume is red. The superhero chose this color because it is associated with his favorite girl, Mary Jane, who has red hair.