O. Henry tells us that life is made up of sobs, sniffles, and smiles, with sniffles predominating. These are the 'stages'. (First stage: sobs; second stage: sniffles; third stage: smiles)
Then he tells us that Della is "gradually subsiding from the first stage to the second". He is telling us that Della has stopped 'howling' (sobbing) and has begun to sniffle. Her violent emotion is subsiding (growing weaker). She is calming down.
I hope this is helpful,