Sometimes the situation will matter. Say, what comes after the "cansar de chorar" determines what kind of "cansaço" you mean.
Basically, we could say that "cansar de chorar" (significando "o coração também chorar") could be: "I cried until I had no tears left left."
Okay, what´s next? Here enters what I meant by "the situation will matter".
I cried until I had no tears left left, then I cried some more. I cried my heart out.
Oh my! Such a tearful, dramatical and emotional sentence...
Read this one: I cried my heart out, it took me a while to get over him (he had dumped her, there was a breakup, etc)/to get over it (the loss of someone or something).
See, what comes next... Is that she shook off those thoughts/the blues and at the end.
And there´s the "se cansar de chorar" in a defiant or turning table way. As shown in the song lyrics:
I had enough of crying, bleeding, sweating, dying
Hear me when I say, gonna live my life everyday
I'm gonna touch the sky, spread these wings and fly
I ain't here to play
Gonna live my life everyday
And also other ways; this is what sprang to mind right now.