(1) If you open the box marked "Two 1g red balls". Take out a red ball and weigh it on the balance. It may be 1g or 2g.
① If the red ball is 1g, the real content of box A is "a red ball of 1g and a red ball of 2g", the real content of box B is "two red balls of 1g" and the real content of two boxes is "two red balls of 2g".
② If it is a 2g red ball, the real content of box A is "two 2g red balls" or "a 1g red ball and a 2g red ball", so it is impossible to make an accurate judgment on its real content.
(2) If you open the box marked "Two 2g red balls". After weighing on the balance, it may be 1g or 2g.
① If it is a red ball of 1g, then the real content of box B is "two red balls of 1g" or "one red ball of 1g and one red ball of 2g", so it is impossible to make an accurate judgment on its real content.
② If it is 2g red ball, then the real content of box B is "one 1g red ball and one 2g red ball", then the real content of box A is "two 2g red balls" and the real content of box C is "two 1g red balls".
According to the analysis of the above two situations, it can be determined that neither the box marked with "two 1g red balls" nor the box marked with "two 2g red balls" has been opened, because neither can fully determine the true contents of these three boxes. So open the box marked "1g red ball, 2g red ball".
If you open the box labeled "one 1g red ball, one 2g red ball", take out another one and weigh it later. It may be 1g red ball or 2g red ball.
① If it is a 1g red ball, then the real content of box C is "two 1g red balls", box B is "one 1g red ball and one 2g red ball", and box A is "two 2g red balls".
② If there are 2g red balls, the real content of box C is "two 2g red balls", box A is "one 1g red ball and one 2g red ball" and box B is "two 1g red balls".
So Xiao Ming opened the box labeled "a 1g red ball, a 2g red ball".