The size of the dime is due to how the United States used silver for subsidiary coinage prior to 1965. The amount of silver in a dime (0.07234 oz) was proportional to the silver content in the larger denominations like quarters (0.18084 oz) and halves (0.36169 oz) and silver dollars (0.77344 oz).
Since 10¢ is 1/5th of 50¢, the half dollar had about 5 times as much silver as the dime; since 25¢ is 2.5 times more than 10¢, the silver content of the quarter is about 2.5x the dime; and so on.
So, the smallness of a dime reflects how much less 10 cents was worth as money—and in terms of silver—than 25 cents, 50 cents, or a dollar.