This symbol is actually composed by two words, two happinesses, or doulbe hapinesses.

Whenever Chinese see this symbol, they would think of a wedding that two persons are getting married, and even more, they would think of the two families are having the happiness of the wedding.

The double-happiness symbol is referring to two happinesses that the two persons and even the two families are getting together to become one family. That's why the two words are put tegother to become one word, the symbol.