This photo from NASA shows the only space suit with double sleeves I’ve seen:
It is a Navy Mark IV pressure suit manufactured by the B.F. Goodrich Company and was modified at the shoulders for the final flight in the Mercury project, flown by Gordon Cooper in 1963. Since 2003 the suit is at the National Air and Space Museum. See this link for details on materials etc:
Pressure Suit, Mercury, Cooper, MA-9, Flown | National Air and Space Museum
The changed construction of the shoulders gave the suit short and long sleeves resembling the Boba Fett flight suit.
Do you think this could have inspired the design of the Boba Fett flight suit? Have you seen other suits with this feature?