면서 울다

cry while doing something else

-(으)면서 puts two actions in the same stretch of time and 울다 is the crying: 마시면서 울면서 (drinking and crying), 애 옷을 보면서 우는 장면 (a scene of crying while looking at her child's clothes). In several lines the first clause is a quotation plus 하면서 — 노래가 안 돼요 하면서 울었던 기억 — meaning the person was saying those words as they cried.

Register: casual, emotional storytelling