Andrew, it's a collective subject acting singly as you show it here. In other words, to sigh doesn't consume my heart all by itself and to cry doesn't either; it is the act of sighing and crying that consumes it. Does the text really say that? I'm hoping for a free translation.
Here's an example:
Getting up in the morning and walking the dog consumes all my energy. By the time I finish with that I'm ready to go back to bed.
Carol