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Peter Parker fought some hella old dudes at the beginning, when he was at his youngest -- the Vulture, The Tinkerer. Disparity in ages was pretty extreme. [I know the Tinkerer was really a Skrull or something.]
J.J.J. was also an old guy. The Lizard was a professor. And of course the Green Goblin wasn't just a metaphorical father figure, but literally the dad of Pete's buddy.
Of course, when you're in high school, most people are older than you. But Pete was surrounded by old/older folks... even on the good side (Aunt May).